Homogeneous Studies of Transiting Extrasolar Planets. II. Physical Properties

Mon. Not. R. Astron. Soc. 000, 000–000 (0000) Printed 2 January 2009 (MN LATEX style ﬁle v2.2)

Homogeneous studies of transiting extrasolar planets. II. Physical properties

John Southworth? Department of Physics, University of Warwick, Coventry, CV4 7AL, UK

2 January 2009

ABSTRACT I present an homogeneous determination of the physical properties of fourteen transiting extrasolar planetary systems for which good photometric and spectroscopic data are available. The input quantities for each system are the results of the light curve analyses presented in Paper I, and published measurements of the stellar velocity amplitude, effective temperature and metal abundance. The physical properties are determined by interpolating within tabulated predictions from stellar theory to find the optimal match to these input data. Statistical uncertainties are found using a perturbation algorithm, which gives a detailed error budget for every output quantity. Systematic uncertainties are assessed for each quantity by comparing the values found using several independent sets of stellar models. As a theory-free alternative, physical properties are also calculated using an empirical mass–radius relation constructed from high-precision studies of low-mass eclipsing binary stars. I find that the properties of the planets depend mostly on parameters measured from the light and radial velocity curves, and have a relatively minor sensitivity to theoretical predictions. In contrast, the orbital semimajor axes and stellar masses have a strong dependence on theoretical predictions, and their systematic uncertainties can be substantially larger than the statistical ones. Using the empirical mass–radius relation instead, the semimajor axes and stellar masses are smaller by up to 15%. Thus our understanding of extrasolar planets is currently limited by our lack of understanding of low-mass stars. Using the properties of all known transiting extrasolar planets, I find that correlations between their orbital periods, masses and surface gravities are significant at the 2–3 σ level. However, the separation of the known planets into two classes according to their Safronov number is weaker than previously found, and may not be statistically significant. Three systems, HAT-P- 2, WASP-14 and XO-3, form their own little group of outliers, with eccentric orbits, massive planets, and stars with masses ∼1.3M¯. The detailed error budgets calculated for each system show where further observations are needed. XO-1 and WASP-1 could do with new transit light curves. TrES-2 and WASP-2 would benefit from more precise stellar temperature and abundance measurements. Veloc- ity measurements of the parent stars are vital for determining the planetary masses: TrES-1, XO-1, WASP-1, WASP-2 and the OGLEs need additional data. The homogeneous analysis presented here is a step towards large-scale statistical studies of transiting extrasolar planetary systems, in preparation for the expected deluge of new detections from CoRoT and Kepler. Key words: stars: planetary systems — stars: binaries: eclipsing — stars: binaries: spectroscopic

1 INTRODUCTION 300 extrasolar planets at the time of writing1. The shortcoming of this technique is that it does not allow us to obtain a detailed under- The discovery of extrasolar planets, made possible through high- standing of individual objects. For each system it is typically pos- precision radial velocity observations of dozens of stars (Mayor & sible to obtain only the orbital period and eccentricity, and lower Queloz 1995), is one of the great scientiﬁc achievements of the limits on the mass and orbital separation of the planet. twentieth century. Radial velocity surveys have have been remark- The detection of the ﬁrst transiting extrasolar planetary sys- ably successful so far (Udry & Santos 2007), discovering nearly

? E-mail: [email protected] 1 See http://exoplanet.eu/ for a list of known extrasolar planets.

°c 0000 RAS 2 John Southworth tem, HD 209458 (Charbonneau et al. 2000; Henry et al. 2000), has crepancy arises from undetectable systematic errors or starspots by demonstrated the solution to this problem. By modelling the light obtaining several independent light curves, each covering the same curve of a transiting extrasolar planetary system (TEP), adding in transit event of a TEP. radial velocity measurements of the star, and adopting one addi- In this work I describe and perform the second stage of the tional constraint from elsewhere, it is possible to determine the analysis: derivation of the physical properties of the fourteen TEPs masses and radii of both the star and planet. This information al- studied in Paper I. This uses the results of the light curve analy- lows the study of the chemical compositions of the two compo- ses, radial velocity measurements, and additional constraints from nents, and thus the formation and evolution of stellar and planetary theoretical stellar model predictions. Several different sets of stel- systems. lar models are used, allowing the systematic error inherent in this Approximately fifty TEPs are currently known, the major- method to be assessed for every output quantity. I also calculate ity discovered through wide-field photometric variability surveys. detailed error budgets for each TEP, showing what further observa- Some estimates of the masses and radii of the components are avail- tions will be useful for each system. As a theory-free alternative to able for each system, but these have been determined in a variety stellar model calculations, I also consider an empirical mass–radius of ways and using a wide range of additional constraints besides relation obtained from high-accuracy studies of 0.2–1.6M¯ eclips- photometric and radial velocity measurements. We are now at the ing binary star systems. The constraints are discussed in Section 2, threshold of statistical studies of the properties of TEPs, for which and applied to each TEP in Section 3. This leads to an homoge- homogeneous analyses are a fundamental requirement. This work neous set of physical properties for the fourteen TEPs (Section 4). is the second instalment of a series of papers intended to provide an Finally, the properties of all known TEPs are compiled and studied homogeneous study of the known TEPs. A recent paper by Torres, in Section 5. Winn, & Holman (2008, hereafter TWH08) has the same goal but differences in the method of analysis, particularly concerning the light curve modelling process. Each individual TEP is here studied in a two-stage process, the first stage being detailed modelling of all available good light 2 METHOD OF ANALYSIS curves of the system, and the second stage being the inclusion of The modelling of a set of light curves of a TEP gives four quanti- 3 additional observational and theoretical information to derive the ties which are important here (Paper I): the orbital period (Porb), physical properties of both star and planet. Whilst the first stage has the inclination of the orbit with respect to the observer (i), and the little or no dependence on theoretical calculations, the second stage, fractional radii of the star and planet, which are defined to be presented here, is reliant on the predictions of stellar evolutionary models. RA Rb rA = rb = (1) In Paper I (Southworth 2008) I tackled stage one: a detailed a a analysis of the light curves of the fourteen TEPs for which good where RA and Rb are the (absolute) stellar and planetary radii and a light curves were then available. The modelling process was per- is the orbital semimajor axis. To first order, there are four quantities 2 formed using the JKTEBOP code (Southworth et al. 2004a,b), that are directly measurable from a transit light curve (separation which represents the components of an eclipsing binary system in time, depth, overall duration and duration of totality) and four using biaxial spheroids (Nelson & Davis 1972; Popper & Etzel derived quantities (Porb, i, rA and rb), so these derived quantities 1981). Random errors were assessed using Monte Carlo simula- are well determined when the available data give the shape of the tions (Southworth et al. 2004c, 2005b) and systematic errors us- transit reliably. The light curve alone does not (apart from Porb) ing a residual-permutation algorithm (Jenkins et al. 2002). Careful have any direct dependence on the absolute scale of the system. thought was give to the treatment of limb darkening: five differ- Note that i is well constrained by a single good light curve, contrary ent limb darkening laws were tried (see Southworth et al. 2007a) to some statements in the literature (see Paper I). and the coefficients of the laws were empirically determined where As well as Porb, i, rA and rb, it is possible to measure the or- possible. Theoretically predicted limb darkening coefficients were bital velocity amplitude of the star, KA, from radial velocity mea- found to be in harmony with those obtained for most TEPs, but surements. However, one additional quantity or constraint is needed were clearly unable to match the results of the highest-quality data to be able to calculate the physical properties of the system. This (Hubble Space Telescope observations of HD 209458). constraint is normally derived from stellar evolution theory, but The results found in Paper I were generally in good agreement in some cases an accurate Hipparcos parallax or angular diame- with published studies, but for both HD 189733 and HD 209458 ter is available which allows stellar theory to be circumvented (e.g. the analysis of several independent light curves gave divergent re- Baines et al. 2007). Alternatively, an empirical mass–radius rela- sults. The discrepancy was the worst for the ratio of the stellar and tion can be used. planetary radii, and amounted to 6.7σ for HD 189733 and 5.6σ for Once this additional constrant has been specified, it is possi- HD 209458. As the ratio of the radii is primarily dependent on the ble to calculate the physical properties of the planet and star: their transit depth, this means either that the available light curves are masses (MA and Mb), radii (RA and Rb), surface gravities (loggA affected by some systematic error which is not noticeable from the and gb), densities (ρA and ρb), and the semimajor axis of the orbit reduced data alone, or that undetected starspots exist on the stellar (a). The interaction with the stellar models also allows an age to be surface. In either case, this disagreement can only be adequately assigned to each TEP based on the properties of the parent star. dealt with if three or more independent light curves are available for a single TEP. It will be possible to determine whether the dis-

3 Throughout this work I identify stellar parameters with a subscripted ‘A’ 2 JKTEBOP is available from and planetary parameters with a subscripted ’b’ to conform to IAU nomen- http://www.astro.keele.ac.uk/ ∼jkt/codes.html clature.

°c 0000 RAS, MNRAS 000, 000–000 Homogeneous studies of transiting extrasolar planets. II. 3

2.1 Constraints from stellar theory the final results in full strength. This choice is unfortunately not as straightforward as it might seem at first glance, because there The mass and radius of the stellar component of a TEP can be con- is a long-standing discrepancy between the observed and predicted strained by comparing its observed effective temperature (Teff), sur- properties of low-mass (0.2–1.1M¯) eclipsing and interferometric face gravity (loggA), and a measure of its metal abundance (here £ Fe ¤ binaries. This disagreement is demonstrated and discussed further taken to be H ), to the predictions of a set of stellar evolutionary £ Fe ¤ in the next section. models. Values for Teff, loggA and H are generally obtained from For this work I have obtained six different sets of stellar model the analysis of high-dispersion spectra of the star, frequently using predictions from five independent groups. The intercomparison of the same observational material as for the radial velocity measure- results obtained using different sets of models allows any system- ments. Knowledge of the stellar parameters then allows the proper- atic differences to be identified and their effects on our under- ties of the planet to be determined. standing of TEPs quantified. References and basic characteristics This procedure often produces imprecise results so can be an of the sets of models are contained in Table 1. Three of the model important source of uncertainty in the final physical properties of sets (Padova, Siess, and Y2) have been calculated with substan- the system (e.g. Alonso et al. 2004; Sato et al. 2005). An improved tial emphasis on accurate modelling of low-mass stars, whereas method is to use the stellar density instead of loggA, which is pre- the other three sets (Cambridge 2000, Cambridge 2007, and Claret) cisely calculable from the results of the light curve analysis (Seager were originally aimed at the study of more massive stars. I am very & Mallen-Ornelas´ 2003) and is a good indicator of the mass of a grateful to Dr. J. Eldridge and Dr. A. Claret for calculating model main sequence star. An excellent discussion and example of this sets at my request. The models of Baraffe et al. (1998) were not process is given by Sozzetti et al. (2007) and Holman et al. (2007b) considered due to their limited coverage in metal abundance. in their study of TrES-2. Whilst the models sets have been calculated by independent The method of analysis used in the present work is to input £ ¤ research groups, there are many similarities in the way physical ef- the measured quantities (P , i, r , r , K , and T and Fe ) into orb A b A eff H fects have been treated so the final results are certainly not indepen- a code for calculating the physical properties of the system (JK- dent. In all six cases the opacities used are from the OPAL group TABSDIM; Southworth et al. 2005a). A reasonable value for the ve- (Rogers & Iglesias 1992; Iglesias & Rogers 1993, 1996) at higher locity amplitude of the planet (K ) is chosen and used to determine b temperatures and from Alexander & Ferguson (1994) at lower tem- a provisional set of physical properties. The code then interpolates peratures. The metal abundances are scaled-solar and use the so- within a tabulated set of stellar model predictions to obtain the ex- lar abundances of Anders & Grevesse (1989), Grevesse & Noels pected stellar radius and T for the provisional stellar mass and £ ¤ eff £ ¤ (1993) or Grevesse et al. (1996). The more recent and controver- Fe . It is done this way because mass and Fe are input quantities H H sial solar chemical composition measurements presented by As- for stellar model codes whereas radius and T are output quanti- eff plund et al. (2006) have not yet been adopted in the stellar models ties. The K is then adjusted until the best match is found to the b used here. Five of the six model sets incorporate moderate convec- model-predicted stellar radius and T . In practise it is difficult to eff tive core overshooting (the exception being Siess) – the differing include the age of the star in the optimisation process because of the implementations means it is not possible to directly compare the strongly nonlinear dependence of stellar properties on age. There- strengths of the effect adopted by the different groups. The Cam- fore the above procedure is performed for a series of ages, starting bridge 2000 models are also available without overshooting, but at 0.1 Gyr and incrementing in 0.1 Gyr chunks until the star has this alternative was not used as I found it made a negligible dif- evolved well beyond the main sequence. The final set of physical ference. The Y2 models are available with enhanced abundances of properties corresponds to the best-fitting stellar radius, T and age. eff the α-elements; to avoid complication this possibility was again not Several notes on this procedure are relevant. (1) Eccentric or- used here. bits can be treated without problem. (2) The velocity amplitude of The procedure in the work has been to derive the physical the planet, K , is used purely as a fitting parameter: its clear phys- b properties of TEPs using each of the model sets separately, allow- ical meaning is not useful as it is not directly observable with cur- ing a clear comparison of the results. To save the reader looking rent technology. (3) Linear interpolation is used within the tables of ahead, I find that the Padova, Y2 and Claret models generally agree model predictions, as it is the most robust and reliable technique. very well, but that the Cambridge 2007 and Siess model sets dis- This in turn requires the model tabulations to have a dense cover- play clear and diverse discrepancies for several TEPs. The Cam- age of parameter space. (4) logg values from spectral analysis A bridge 2000 models are not available for masses below 0.5M or are not used as constraints because there are questions over the ¯ for metal abundances above Z = 0.03 so cannot be used for many reliability of this procedure (for example see the conflicting ob- of the TEPs studied here. I have therefore used the Padova, Y2 and servational results for XO-3; Johns-Krull et al. 2008; Winn et al. Claret models for the final results presented below, in an attempt to 2008b). (5) The very slow evolutionary timescales of K dwarfs and reach consensus and to show how important systematics are even M dwarfs means that their ages are essentially unconstrained and in between models which seem to be in happy agreement. I have fur- fact have a negligible effect on the results. G and F dwarfs evolve thermore adopted the Claret models as the baseline set, and used more quickly, meaning their evolutionary state has a significant ef- the results from the other two model sets to infer the systematic er- fect on the results, and can therefore be determined more precisely. rors present in the physical properties. This is because the Padova (6) The procedure implicitly applies the constraint on the stellar models do not stretch to high enough metal abundances to cover density obtained from the light curve modelling process. all of the TEPs studied in this work, and also to provide some variety compared to most literature studies which consider only the Y2 models. 2.1.1 Which theoretical stellar evolutionary predictions to use? This is the first time that systematic uncertainties have been The method outlined above of determining the properties of TEP presented for the full set of physical properties of a sample of TEPs. has a clear dependence on stellar models. It is consequently impor- However, they should be treated with some caution as they are tant to use a reliable set of models, as any errors will propagate into based on only three different sets of stellar models. Work is under-

°c 0000 RAS, MNRAS 000, 000–000 4 John Southworth

Table 1. Physical ingredients and coverage of the stellar models used in this work. Note that the Cambridge 2007 and Claret model sets are extensions to lower masses which were calculated upon request (J. Eldridge, 2007, private communication; A. Claret, 2007, private communication). To ensure homogeneity, these calculations have not been supplemented with previously published models. Four columns give some physical quantities adopted by the model sets: Yini is the primordial helium abundance, ∆Y/∆Z is the helium-to-metals enrichment ratio, Z¯ is the solar metal abundance (fraction by mass) and αMLT is the mixing length parameter.

Model set Reference Range in Range in metal Yini ∆Y Z¯ αMLT Notes mass (M¯) abundance (Z) ∆Z

Padova Girardi et al. (2000) 0.15 to 7.0 0.0004 to 0.03 0.23 2.25 0.019 1.68 Siess Siess et al. (2000) 0.1 to 7.0 0.01 to 0.04 0.235 2.1 0.02 1.605 Includes pre-MS phase Y2 Demarque et al. (2004) 0.4 to 5.2 10−5 to 0.08 0.23 2.0 0.02 1.743 Scaled-solar abundances Cambridge 2000 Pols et al. (1998) 0.5 to 50 10−4 to 0.03 0.24 2.0 0.0188 2.0 Models with overshooting Cambridge 2007 Eldridge & Tout (2004) 0.5 to 2.0 0.01 to 0.05 0.24 2.0 0.0188 2.0 Calculated for this work Claret Claret (2004, 2005, 2006, 2007) 0.2 to 1.5 0.01 to 0.05 0.24 2.0 0.02 1.68 Calculated for this work way to improve the situation for later papers in this series. TWH08 To construct an empirical mass-radius relation for low-mass presented an homogeneous study of 23 TEPs in which both the Y2 stars I have compiled the physical properties of all stars in eclips- 4 and Padova models were used, and found no major differences being binaries which have masses of M < 1.6M¯, and masses and tween the results. radii determined to accuracies of no worse than 3%. These data are supplemented by the Sun and are given in Table 2. The sample of well-studied eclipsing binaries is biased towards more evolved systems (Andersen 1991) because they are brighter, and their larger 2.2 Empirical mass–radius–Teff relations from eclipsing binary stars radii means that there is a greater probability that they will eclipse. This bias basically affects only those stars with M & 1 M¯, due The main drawback to using theoretical stellar models in the deriva- to age effects, but must be removed from the sample. A simple tion of the physical properties of TEPs is that any shortcomings of cut in logg could be used to reject more evolved systems, but the the models propagate directly into systematic errors in the result- particular choice of cut has a substantial effect on the resulting ing TEP parameters. This is particularly worrying because there is a mass–radius relation. Instead, for eclipsing binaries consisting of clear discrepancy between the predicted and observed properties of two >1 M¯ stars, I have used only the secondary component and M 0.2–1.1M¯ stars. Our primary source of information on the prop- also imposed the requirement that the mass ratio q = B < 0.9. MA erties of normal stars is the study of eclipsing binaries, where it is In this way the secondary star is guaranteed to be only part-way possible to measure the masses and radii of stars empirically and through its main sequence lifetime, because if it were not then the to accuracies of 1% or better (e.g. Lacy et al. 2008; Southworth & primary star would have evolved to or beyond the giant stage. This Clausen 2007). procedure allows the construction of a sample of stars which are The radii of low-mass eclipsing binary stars are observed to be unevolved without making a direct and statistically problematic cut larger than predicted by theoretical models, by up to 15% (Hoxie to reject evolved ones. As an example, TZ Men A is a 2.5M¯ main 1973; Clausen 1998; Torres & Ribas 2002; Ribas et al. 2008c). sequence star so must have an age below about 0.5 Gyr. This means Their Teffs are correspondingly smaller, as the predicted luminosi- that TZ Men B (see Table 2) must be no older than 20% of its total ties are close to those observed. There is a gathering consensus main sequence lifetime of roughly 2.4 Gyr. that this discrepancy is due to stellar activity (Ribas 2006; Lopez-´ The above criteria result in the sample of eclipsing binary Morales 2007; Chabrier et al. 2007), which is stronger in quickly- star components given in Table 2. V1229 Tau B was included as its rotating stars such as young ones (Morales et al. 2008) and those membership of the Pleiades provides independent evidence that it in eclipsing binaries. A different conclusion was reached by Berger is unevolved (Groenewegen et al. 2007; Southworth et al. 2005a). et al. (2006), whose interferometric observations showed that the The resulting sample of 29 stars in eclipsing binaries (plus the Sun) radius discrepancy existed in a sample of slowly-rotating field M covers the masses 0.214 M¯ to 1.586 M¯ and – apart from any ef- dwarfs and was correlated with metallicity (a surrogate for opac- fects due to binarity – is representative of low-mass stars in the ity). The radius discrepancy was also found for the host star of the Solar neighbourhood. TEP GJ 436, despite this being a slowly-rotating and inactive M Low-order polynomials have been fitted to the data in Table 2 dwarf (Torres 2007). to define mass–radius and mass–Teff relations. The scatter around As an alternative to the use of stellar models, in this work I the relations is much larger than the measurement errors, demon- present physical properties of TEPs calculated using a stellar mass– strating that the stars in the sample have substantial ‘cosmic scatter’ radius relation constructed from well-studied eclipsing binaries. due to differing evolutionary stage, chemical composition, activity This procedure is actually much simpler than the one using stellar level and other properties between stars. The measurement errors models (outlined in Section 2.1), and requires only that the value of were therefore not used in calculating the final relations. A first- Kb (the orbital velocity amplitude of the planet) is chosen for which order polynomial (straight line) is a satisfactory fit to the mass– the stellar properties satisfy a given mass–radius relation. Varia- radius relation, and results in: tions in age and metallicity cannot be accommodated because such R = (0.00676 ± 0.03408) + (1.01824 ± 0.03368) · M (2) values are not in general directly observable for low-mass eclipsing binaries. Instead, the stellar components of the TEPs are assumed to represent the same stellar population as the stars in eclipsing bi- 4 A catalogue of well-studied eclipsing binary systems is available at naries. http://www.astro.keele.ac.uk/ ∼jkt/debdata/debs.html

°c 0000 RAS, MNRAS 000, 000–000 Homogeneous studies of transiting extrasolar planets. II. 5

Table 2. Properties of the sample of stars used to determine the empirical mass–radius and mass–Teff relations.

Star Mass (M¯) Radius (R¯) logTeff (K) Reference CM Dra B 0.2135 ± 0.0010 0.2347 ± 0.0019 3.498 ± 0.014 Metcalfe et al. (1996) CM Dra A 0.2306 ± 0.0011 0.2516 ± 0.0020 3.498 ± 0.014 Metcalfe et al. (1996) CU Cnc B 0.3980 ± 0.0014 0.3908 ± 0.0094 3.495 ± 0.021 Ribas (2003) CU Cnc A 0.4333 ± 0.0017 0.4317 ± 0.0052 3.500 ± 0.021 Ribas (2003) NSVS 010317 B 0.4982 ± 0.0025 0.5088 ± 0.0030 3.546 ± 0.004 Lopez-Morales et al. (2007) NSVS 010317 A 0.5428 ± 0.0027 0.5260 ± 0.0028 3.558 ± 0.008 Lopez-Morales et al. (2007) YY Gem A 0.5975 ± 0.0047 0.6196 ± 0.0057 3.582 ± 0.011 Torres & Ribas (2002) YY Gem B 0.6009 ± 0.0047 0.6036 ± 0.0057 3.582 ± 0.011 Torres & Ribas (2002) GU Boo B 0.599 ± 0.006 0.620 ± 0.020 3.581 ± 0.015 Lopez-Morales´ & Ribas (2005) GU Boo A 0.610 ± 0.007 0.623 ± 0.016 3.593 ± 0.014 Lopez-Morales´ & Ribas (2005) 2MASS J05162881+2607387 B 0.770 ± 0.009 0.817 ± 0.010 3.618 ± 0.025 Bayless & Orosz (2006) 2MASS J05162881+2607387 A 0.787 ± 0.012 0.788 ± 0.015 3.623 ± 0.020 Bayless & Orosz (2006) RW Lac B 0.870 ± 0.004 0.964 ± 0.004 3.745 ± 0.012 Lacy et al. (2005) HS Aur B 0.879 ± 0.017 0.873 ± 0.024 3.716 ± 0.006 Popper et al. (1986) HS Aur A 0.900 ± 0.019 1.004 ± 0.024 3.728 ± 0.006 Popper et al. (1986) V1061 Cyg B 0.9315 ± 0.0068 0.974 ± 0.020 3.724 ± 0.012 Torres et al. (2006) FL Lyr B 0.960 ± 0.012 0.962 ± 0.028 3.724 ± 0.008 Popper et al. (1986) Sun 1.0 1.0 3.762 ± 0.001 Smalley (2005) V432 Aur A 1.080 ± 0.014 1.230 ± 0.006 3.825 ± 0.006 Siviero et al. (2004) EW Ori A 1.194 ± 0.014 1.141 ± 0.011 3.776 ± 0.007 Popper et al. (1986) HS Hya B 1.2186 ± 0.0070 1.2161 ± 0.0071 3.806 ± 0.003 Torres et al. (1997) AD Boo B 1.237 ± 0.013 1.211 ± 0.018 3.775 ± 0.007 Lacy (1997) HS Hya A 1.2552 ± 0.0078 1.2747 ± 0.0072 3.813 ± 0.003 Torres et al. (1997) HD 71636 B 1.285 ± 0.007 1.361 ± 0.008 3.809 ± 0.009 Henry et al. (2006) YZ Cas B 1.350 ± 0.010 1.348 ± 0.015 3.826 ± 0.016 Lacy (1981) V442 Cyg B 1.410 ± 0.023 1.662 ± 0.033 3.833 ± 0.006 Lacy & Frueh (1987) FS Mon B 1.462 ± 0.010 1.629 ± 0.012 3.816 ± 0.007 Lacy et al. (2000) TZ Men B 1.504 ± 0.010 1.432 ± 0.015 3.857 ± 0.018 Andersen et al. (1987) GV Car B 1.540 ± 0.020 1.430 ± 0.060 3.889 ± 0.019 Southworth & Clausen (2006) V1229 Tau B 1.586 ± 0.042 1.565 ± 0.015 3.861 ± 0.022 Groenewegen et al. (2007) where M and R represent stellar mass and radius in solar units. The system. Following a request from the referee, I now show how im- quoted uncertainties are 1σ errors and the rms scatter about the best portant this extra constraint is for each of the physical properties. fit is 0.073 R¯. A large number of significant figures are deliber- The directly observed quantities from the light and velocity ately included, to avoid problems with rounding off. The mass–Teff curves are Porb, K1, e, rA, rb and i, where e represents the orbital relation requires a third-order polynomial to get a good fit, and is: eccentricity. The extra constraint is derived from several observable and theoretical inputs, which in the current approach are combined Teff = (3217 ± 564) − (2427 ± 2304) · M to specify the quantity Kb. Thus the specification of Kb contains +(7509 ± 2802) · M2 − (2771 ± 1030) · M3 (3) all of the indirect constraints which depend on the stellar models (or empirical mass–radius relations) used. Any model-dependent where the rms scatter about the best fit is 328 K. The mass–T eff systematic errors will act on K and so infect most of the quantities relation is less robust than the mass–radius relation due to the large b below. variety of ways in which T s have been observationally measured. eff From Kepler’s third law and the definitions of fractional ra- I therefore do not consider the mass–T relation further. eff dius, surface gravity and density, the investment of a small amount The mass–radius and mass–T relations are compared to the eff of algebra results in the following equations for the semimajor axis eclipsing binary data in Fig. 1. These data are also contrasted in and the properties of the star and planet. The equations are in the Fig. 2 with the predictions of the six sets of stellar evolutionary S.I. system so do not include scaling factors to account for the use models used in this work. It can be seen that the agreement be- of astronomical units. tween theory and observation is poor, particularly in the interval 0.7–1.0M¯. The agreement seems to be better at lower masses, but µ ¶ 2 1 P (1 − e ) 2 the radius discrepancy is still visible in new results for the 0.22 M a = a + a = orb (K + K ) (4) ¯ A b 2π sini A b eclipsing binary CM Dra (Dr. I. Ribas, private communication).

µ ¶ 2 3 1 Porb (1 − e ) 2 2 2.3 Physical properties and the pervasive inﬂuence of MA = (KA + Kb) Kb (5) G 2π sin3 i systematic errors The previous two sections have discussed how to obtain the ex- µ ¶ 2 3 tra constraint which is needed to transform the directly measured 1 Porb (1 − e ) 2 2 Mb = (KA + Kb) KA (6) quantities into the physical properties of the star and planet for each G 2π sin3 i

°c 0000 RAS, MNRAS 000, 000–000 6 John Southworth

Figure 1. Mass–radius and mass–Teff diagrams showing the sample of stars Figure 2. Mass–radius and mass–Teff diagrams comparing the observed given in Table 2. The ﬁlled circles show the properties of stars in eclipsing properties of low-mass eclipsing binaries and the Sun to theoretical model binary systems and the Sun is represented by a ¯. The solid lines represent predictions. The symbols are as in Fig 1. The lines show the predictions the mass–radius and mass–Teff relations obtained from the data (see text for of the six sets of stellar models used in this work, for an age of 1 Gyr details). and an approximately solar chemical composition. Solid lines show predictions from the model sets used for the ﬁnal results (Padova, Y2 and Claret) and dashed lines show predictions from other the model sets considered in µ ¶ 2 1 P (1 − e ) 2 this work (Cambridge 2000, Cambridge 2007, Siess). Note that the models R = r a = orb r (K + K ) (7) A A 2π sini A A b do not match the solar properties as they are calculated for an age much younger than that of the Sun. µ ¶ 2 1 P (1 − e ) 2 R = r a = orb r (K + K ) (8) b b 2π sini b A b When interpreting these equations it must be remembered −1 that KA is generally a few hundred m s and Kb is typically −1 µ ¶ 2 1 150 km s . Representing the uncertainty in a quantity x as σ(x), GMA 2π (1 − e ) 2 Kb gA = 2 = 2 (9) this means that: RA Porb sini rA KA + Kb ≈ Kb σ(KA + Kb) ≈ σ(Kb) (13) µ ¶ 2 1 GMb 2π (1 − e ) 2 KA and gb = = (10) µ ¶ R 2 P sini r 2 K K b b b ≈ 1 σ b → 0 (14) KA + Kb KA + Kb µ ¶2 GMA 2π 1 Kb Two properties can be picked out which depend mainly on Kb ρA = 3 = 3 (11) RA Porb rA (KA + Kb) and thus are strongly affected by model-dependent systematic errors: a and MA. In the usual case where Porb and sini have a negli- µ ¶2 gible uncertainty and e is assumed to be zero, the relation in Eq. 13 GMb 2π 1 KA ρb = 3 = 3 (12) means that the precisions of a and MA depend only on the precision Rb Porb rb (KA + Kb) of Kb. It is important to remember that both a and MA have quite a where Eq. 10 is taken from Southworth et al. (2007b). strong dependence on the measured rA: this is not explicit in Eqs. 4

°c 0000 RAS, MNRAS 000, 000–000 Homogeneous studies of transiting extrasolar planets. II. 7 and 5 but happens because rA has an important role in determining of TWH08 and Dr. B. Smalley (private communication). These lim- Kb (Section 2.1). its transpire from studies of the reliability of the Teff scale for FGK The other properties of the star are less affected by systematic dwarfs (e.g. Ram´ırez & Melendez´ 2005a,b), and the fact that Teff £ Fe ¤ errors. RA and gA are proportional to Kb but also depend on rA. In and H are significantly correlated in spectral synthesis analyses general, the uncertainty in rA dominates that in Kb so the model de- (e.g. Buzzoni et al. 2001; Holman et al. 2007a). pendence is less important than the quality of the light curve. ρA is The analyses are presented below for the same fourteen TEPs a special case as its dependence on outside constraints is negligible as in Paper I, and following strictly the same order as that work. (Eq. 11 and Eq. 14), as is already well known (Seager & Mallen-´ Example full error budgets are presented for the first and last TEPs Ornelas 2003). (TrES-1 and HD 209458). The planetary surface gravity is speci- The properties of the planet are all in general more strongly fied completely by parameters measured from the light and radial affected by the quality of the observations than by the model- velocity curves (Southworth et al. 2004c, 2007b) so has no depen- 5 dependent systematics. This is the case for Rb and ρb for all the dence on theoretical models or mass–radius relations . The stellar TEPs discussed here. The situation for the planet’s mass is more density is similarly almost totally free of theoretical dependence 2 complicated: using Eq. 14 gives Mb ∝ KAKb . Whilst Kb is typi- (Seager & Mallen-Ornelas´ 2003), the ‘almost’ stemming from the cally known to a precision of 1.5%, KA is measured to accuracies requirement that the mass of the planet is negligible compared to of between 1.2% and 30% for these TEPs. In most cases the un- that of the star. 2 certainty in KA dominates that in Kb , so the model-dependence of In this sort of study is it is important to compare the results the properties of the planet is relatively unimportant. The surface against literature determinations, to find and investigate any dis- gravity of the planet, gb, is a special case as it is only dependent on crepancies. The resulting tables of results are bulky and have been observable quantities so can be freed from any influence of system- exiled to the Appendix (electronic only). atic errors (Southworth et al. 2004c, 2007b).

3.1 TrES-1 2.4 Error analysis TrES-1 was discovered to be a TEP by the Trans-Atlantic Exo- A robust error analysis method is a vital tool in high-precision stud- planet Survey (Alonso et al. 2004). An excellent z-band light curve ies. The error analysis is performed using the JKTABSDIM code by of TrES-1, obtained by Winn et al. (2007b) and chosen for analysis perturbing every input parameter by its uncertainty, whilst keeping in Paper I, gives the fractional radii of the star and planet to 2% and all other parameters at their input values, to measure the effect it 3%, respectively. The physical properties of the two components has on all output quantities. The resulting individual error contri- and of the system have been calculated using five sets of stellar 2 butions are summed in quadrature to provide a final uncertainty for models (Padova, Siess, Y , Cambridge 2007, and Claret) and are each of the physical properties calculated by JKTABSDIM. The un- listed in Table 5. 2 certainty in the mass–radius relation is taken to be the 1σ errors on The agreement between three sets of models (Padova, Y and the two coefficients. Claret) is good, but the other two models are slightly discrepant and From the full error budget calculated by the above procedure, predict very young ages which are towards the edge of the range of it is possible to see for each system exactly how much effect each possible ages. The ages found for the three good sets of models input quantity has on the final uncertainties, and therefore what ob- agree to within their (rather large) errors; note that it is possible to servations could be taken to improve the measurement of the phys- have a larger errorbar than value for age because individual error ical properties for each system. As Kb is used as a fitting parameter, contributions are added in quadrature. The age of TrES-1 is therefore constrained only to be less than about 5.5 Gyr. A comparison its output uncertainty is a measure of the uncertainty in the stellar£ ¤ Fe with published results is available in the Appendix (Table A1) and properties resulting from the observational errors in Teff and H . Example error budgets are given below for the TEPs TrES-1 and shows a reasonable agreement. HD 209458. The physical properties found using the eclipsing binary As a general rule, if the input parameters have symmetric er- mass–radius relation (Eq. 2) are quite different to those found using rors, the resulting output parameters also have approximately sym- stellar models, as TrES-1 A is in the mass regime where models and metric uncertainties. In some cases the light curve analyses in Pa- observational data match poorly (Fig. 1). The discrepancy amounts per I resulted in separate upper and lower error estimates for the to 15% in MA, 6% in RA, 13% in Mb and 6% in Rb. The stellar and photometric parameters, which propagate through into asymmet- planetary masses are thus much more strongly affected than their ric error estimates for the quantities calculated in this work. The respective radii. The planet’s surface gravity, gb, is not affected be- exception is the model-derived stellar age, which has asymmetric cause this depends only on observed properties (Southworth et al. errorbars in almost all cases. 2004c, 2007b), but the planet density is affected by 6%. It is important to note that this disagreement is a manifestation of the radius discrepancy seen in low-mass eclipsing and field stars (Section 2.2), so is a fundamental limitation due to the current state of knowledge 3 PHYSICAL PROPERTIES OF THE TEPS in stellar astrophysics. Until this discrepancy can be cleared up, we

The analyses presented in this work require measurements of Porb, i, r and r from transit light curve modelling. These measurements A b 5 The literature contains statements that calculation of planetary surface were obtained in Paper I and are given in Table 3. The analyses also £ Fe ¤ gravity is ‘almost’ or ‘virtually’ independent of theoretical calculations. It require values for the stellar properties KA, Teff and H . These is actually totally independent – depending on how limb darkening is ac- have been taken from the literature, and are listed and referenced in counted for in the light curve analysis – and is applicable to any opaque £ Fe ¤ Table 4. The minimum uncertainties in Teff and H have been set and approximately circular body, including stars, planets, moons, and ten- at 50 K and 0.05 dex, respectively, following the recommendations nis balls.

°c 0000 RAS, MNRAS 000, 000–000 8 John Southworth

Table 3. Parameters from the light curve modelling presented in Paper I and used in this work.

System Orbital period (days) Orbital inclination (degrees) Fractional stellar radius, rA Fractional planetary radius, rb TrES-1 3.030065 88.67 ± 0.71 0.0964 ± 0.0018 0.01331 ± 0.00035 TrES-2 2.47063 83.71 ± 0.42 0.1296 ± 0.0038 0.01643 ± 0.00046 XO-1 3.941534 89.06 ± 0.84 0.0886 ± 0.0019 0.01166 ± 0.00035 +0.0057 +0.0007 WASP-1 2.519961 88.0 ± 2.0 0.1737−0.0089 0.0182−0.0011 WASP-2 2.152226 84.83 ± 0.53 0.1245 ± 0.0058 0.01635 ± 0.00093 HAT-P-1 4.46543 86.26 ± 0.24 0.0930 ± 0.0028 0.01043 ± 0.00033 OGLE-TR-10 3.101278 83.87 ± 0.69 0.157 ± 0.009 0.0182 ± 0.0011 OGLE-TR-56 1.211909 79.8 ± 2.4 0.245 ± 0.026 0.0241 ± 0.0034 OGLE-TR-111 4.0144479 88.11 ± 0.66 0.0842 ± 0.0038 0.01107 ± 0.00067 OGLE-TR-132 1.689868 83.3 ± 2.4 0.211 ± 0.020 0.0198 ± 0.0024 GJ 436 2.64385 86.43 ± 0.18 0.0731 ± 0.0027 0.00605 ± 0.00023 +0.012 +0.011 HD 149026 2.8758882 88.0 ± 2.0 0.140−0.006 0.0068−0.008 HD 189733 2.2185733 85.78 ± 0.25 0.1113 ± 0.0031 0.0175 ± 0.0005 HD 209458 3.52474859 86.590 ± 0.046 0.11384 ± 0.00041 0.01389 ± 0.00006

Table 4. Measured quantities for the parent stars which were adopted in the analysis presented in this work.

£ ¤ −1 Fe System Velocity amplitude ( m s ) Teff (K) Reference H Reference TrES-1 115.2 ± 6.2 Alonso et al. (2004) 5226 ± 50 Santos et al. (2006) 0.06 ± 0.05 Santos et al. (2006) TrES-2 181.3 ± 2.6 O’Donovan et al. (2006) 5850 ± 50 Sozzetti et al. (2007) −0.15 ± 0.10 Sozzetti et al. (2007) XO-1 116.0 ± 9.0 McCullough et al. (2006) 5750 ± 50 McCullough et al. (2006) 0.015 ± 0.05 McCullough et al. (2006) WASP-1 114 ± 13 Collier Cameron et al. (2007) 6110 ± 50 Stempels et al. (2007) 0.23 ± 0.08 Stempels et al. (2007) WASP-2 155 ± 11 Collier Cameron et al. (2007) 5200 ± 200 Collier Cameron et al. (2007) 0.00 ± 0.15 (assumed) HAT-P-1 60.3 ± 2.1 Bakos et al. (2007a) 5975 ± 50 Bakos et al. (2007a) 0.13 ± 0.05 Bakos et al. (2007a) OGLE-TR-10 80 ± 17 Konacki et al. (2005) 6075 ± 86 Santos et al. (2006) 0.28 ± 0.10 Santos et al. (2006) OGLE-TR-56 212 ± 22 Bouchy et al. (2005a) 6119 ± 62 Santos et al. (2006) 0.25 ± 0.08 Santos et al. (2006) OGLE-TR-111 78 ± 14 Pont et al. (2004) 5044 ± 83 Santos et al. (2006) 0.19 ± 0.07 Santos et al. (2006) OGLE-TR-132 141 ± 42 Bouchy et al. (2004) 6210 ± 59 Gillon et al. (2007c) 0.37 ± 0.07 Gillon et al. (2007c) GJ 436 18.34 ± 0.52 Maness et al. (2007) 3350 ± 300 Maness et al. (2007) −0.03 ± 0.2 Bonfils et al. (2005) HD 149026 43.3 ± 1.2 Sato et al. (2005) 6147 ± 50 Sato et al. (2005) 0.36 ± 0.05 Sato et al. (2005) HD 189733 205 ± 6 Bouchy et al. (2005b) 5050 ± 50 Bouchy et al. (2005b) −0.03 ± 0.05 Bouchy et al. (2005b) HD 209458 85.1 ± 1.0 Naef et al. (2004) 6117 ± 50 Santos et al. (2004) 0.02 ± 0.05 Santos et al. (2004) cannot claim to measure the parameters of TEPs to better than the mass and the orbital separation (a). It is reassuring that the effect £ Fe ¤ percentages given above (depending on the system). Thus our un- of Teff and H is relatively limited for our understanding of the derstanding of planets is limited by our understanding of low-mass properties of the planet. stars. The error budget for the calculations involving the mass– radius relation (Table 7) is similar to that using stellar models. As 3.1.1 Error budget a general rule, the final results are less accurate as the uncertainty in the coefficients of£ the¤ relation is more important than the un- The analysis procedure used here (see Section 2.1) yields a full er- Fe certainty in Teff and H . These coefficients therefore take on a ror budget detailing the effect on each input parameter on each out- more important role in calculation of the physical properties, and put quantity. For TrES-1 I include these error budgets to give an ex- dominate the uncertainties in a and MA. The effect of uncertainties ample of what information can be grasped from such numbers. The on the observed input quantities (KA, i, rA, rb) are consequently error budget calculated using the Padova stellar models is given in less important. This effect would be even stronger if the ‘cosmic Table 6 and using the mass–radius relation in Table 7. scatter’ in the calculation were included in full strength (i.e. if the From Table 6 it can be seen that the uncertainty in the orbital uncertainty in the mass–radius calibration did not decrease with the inclination (i) is totally unimportant to the calculated quantities. inclusion of more data). The uncertainty in KA dominates the uncertainty in Mb, and is important also for gb and ρb. Unsurprisingly, rA is a vital input in The final conclusions of this section are that the best way to calculating the physical properties of the star, in particular its age improve our knowledge of the parameters of the planet is to get a and density, and rb is similarly critical to our understanding of the better measurement for rb. Similarly, a more precise rA is needed to planet’s properties. Of most interest is the effect of uncertainty in better understand the star. As these quantities are already accurately £ Fe ¤ Teff and H – the quantities which provide the all-important final measured, it will need a very good light curve to improve this situ- constraint for calculation of the full physical properties of the sys- ation. However, a more accurate measurement of KA is well within tem. These are relevant for most of the output quantities, but are by reach and would much improve the measurement of the mass of the a long way the most important input for calculation of the stellar planet.

°c 0000 RAS, MNRAS 000, 000–000 Homogeneous studies of transiting extrasolar planets. II. 9

Table 5. Derived physical properties for the TrES-1 system. a is the orbital semimajor axis. The stellar mass, radius, gravity and density are denoted by MA, RA, loggA and ρA, respectively. The corresponding planetary quantities are given by Mb, Rb, gb and ρb.

Mass–radius Padova models Siess models Y2 models Cambridge 2007 Claret models

a (AU) 0.0373 ± 0.0011 0.03954 ± 0.00036 0.04035 ∗ ± 0.00023 0.03946 ± 0.00034 0.03942 ± 0.00017 0.04000 ± 0.00043 ∗ MA (M¯) 0.752 ± 0.066 0.897 ± 0.025 0.954 ± 0.016 0.892 ± 0.023 0.890 ± 0.012 0.929 ± 0.030 ∗ RA (R¯) 0.772 ± 0.031 0.819 ± 0.015 0.836 ± 0.020 0.818 ± 0.015 0.817 ± 0.015 0.829 ± 0.015 ∗ loggA (cgs) 4.539 ± 0.017 4.564 ± 0.018 4.573 ± 0.014 4.563 ± 0.018 4.563 ± 0.016 4.569 ± 0.018 ∗ ρA (ρ¯) 1.632 ± 0.093 1.632 ± 0.092 1.632 ± 0.092 1.632 ± 0.092 1.632 ± 0.092 1.632 ± 0.092 ∗ Mb (MJup) 0.678 ± 0.054 0.763 ± 0.043 0.795 ± 0.044 0.760 ± 0.043 0.759 ± 0.041 0.781 ± 0.045 ∗ Rb (RJup) 1.038 ± 0.041 1.101 ± 0.031 1.124 ± 0.030 1.099 ± 0.030 1.098 ± 0.029 1.114 ± 0.032 −2 gb ( m s ) 15.6 ± 1.2 15.6 ± 1.2 15.6 ± 1.2 15.6 ± 1.2 15.6 ± 1.2 15.6 ± 1.2 ∗ ρb (ρJup) 0.606 ± 0.060 0.572 ± 0.055 0.560 ± 0.054 0.573 ± 0.055 0.573 ± 0.055 0.565 ± 0.054 +3.9 ∗ +0.0 +2.1 +1.8 +4.1 Age (Gyr) 1.0−1.6 0.1 −0.0 3.4−2.1 0.1−0.0 1.2−1.8

∗ These quantities have been calculated using stellar models for stars with small ages. Their values and uncertainties may therefore be unreliable due to edge effects within the grid of model tabulations.

−2 Table 8. Derived physical properties for TrES-2. The symbols are as in Table 5. In every case the planetary surface gravity is gb = 19.9 ± 1.2 m s and the stellar density is ρA = 1.008 ± 0.092ρ¯.

Mass–radius Padova models Siess models Y2 models Cambridge 2007 Claret models

a (AU) 0.0352 ± 0.0010 0.03537 ± 0.00061 0.03666 ± 0.00063 0.03559 ± 0.00051 0.03708 ± 0.00024 0.03568 ± 0.00056

MA (M¯) 0.958 ± 0.081 0.966 ± 0.050 1.075 ± 0.056 0.984 ± 0.043 1.113 ± 0.022 0.991 ± 0.047 RA (R¯) 0.983 ± 0.049 0.985 ± 0.031 1.021 ± 0.032 0.991 ± 0.031 1.033 ± 0.033 0.994 ± 0.031 loggA (cgs) 4.435 ± 0.022 4.436 ± 0.028 4.451 ± 0.028 4.439 ± 0.027 4.456 ± 0.025 4.440 ± 0.027

Mb (MJup) 1.180 ± 0.069 1.186 ± 0.045 1.274 ± 0.048 1.201 ± 0.039 1.303 ± 0.026 1.206 ± 0.042 Rb (RJup) 1.213 ± 0.048 1.216 ± 0.040 1.260 ± 0.041 1.224 ± 0.039 1.275 ± 0.037 1.226 ± 0.040 ρb (ρJup) 0.662 ± 0.060 0.660 ± 0.057 0.636 ± 0.055 0.655 ± 0.057 0.629 ± 0.054 0.654 ± 0.057 +1.9 +1.3 +1.2 +1.6 Age (Gyr) 4.5 ± 2.1 1.5−2.0 4.5−1.7 0.1−0.1 5.3−2.6

Table 6. Detailed error budget for the calculation of the system properties Table 7. Detailed error budget for the calculation of the system properties of TrES-1 from the light curve parameters, stellar velocity amplitude, and of TrES-1 from the light curve parameters, stellar velocity amplitude, and the predictions of the Padova stellar models. Each number in the table is the mass–radius relation. The layout of the table is the same as that for Table 6. fractional contribution to the final uncertainty of an output parameter from The quantities MR0 and MR1 refer to the constant and linear coefficients the errorbar of an input parameter. The final uncertainty for each output of the mass–radius relation. parameter (not given) is the quadrature sum of the individual contributions from each input parameter. Whilst the orbital period is an input parameter, Output Input parameter it is not included here as its uncertainty too small to register. parameter KA i rA rb MR0 MR1 a 0.001 0.321 0.760 0.564 Output Input parameter £ ¤ Fe MA 0.321 0.760 0.565 parameter KA i rA rb Teff H RA 0.001 0.710 0.565 0.419 Age 0.737 0.468 0.468 loggA 0.001 0.706 0.568 0.421 a 0.002 0.336 0.715 0.542 ρA 0.001 1.000

MA 0.335 0.715 0.542 Mb 0.675 0.004 0.237 0.561 0.417 RA 0.001 0.886 0.367 0.278 Rb 0.001 0.239 0.666 0.567 0.421 loggA 0.001 0.980 0.159 0.121 gb 0.715 0.004 0.699 ρA 0.001 1.000 ρb 0.537 0.003 0.094 0.790 0.224 0.166 Mb 0.945 0.005 0.107 0.229 0.173 Rb 0.001 0.110 0.943 0.234 0.177 gb 0.715 0.004 0.699 ρb 0.560 0.003 0.032 0.823 0.068 0.052 obtained from a light curve of a given quality. TrES-2 is also £ Fe ¤ unusual in that the star has a subsolar metal abundance ( H = −0.15 ± 0.10; Sozzetti et al. 2007). In Paper I the analysis of the z-band transit light curve from Holman et al. (2007b) resulted in 3.2 TrES-2 measurements of rA and rb to 3%. The second TEP discovered by the TrES survey (O’Donovan et al. The physical properties of TrES-2 are presented in Table 8, 2006) is of interest because its relatively low orbital inclination where good agreement is again found between the Padova, Y2 (high impact parameter) means that more accurate results can be and Claret models for ages around 5 Gyr. As before, the Cam-

°c 0000 RAS, MNRAS 000, 000–000 10 John Southworth bridge 2007 and Siess models predict a smaller radius for a given inclination allows more precise measurements of rA and rb. Unfor- mass in this mass regime, resulting in overall larger values for the tunately, the stellar Teff measurement is accurate to only ±200 K, physical properties. The mass–radius relation result differs in the and no metal abundance measurement is available. As “the abun- opposite sense, but this time provide a reasonable agreement with dances do not appear to be substantially different from solar” (Col- £ Fe ¤ the calculations involving theoretical predictions. The agreement lier Cameron et al. 2007), I have here adopted H = 0.00±0.15 (a between the calculations involving the Padova, Y2 and Claret mod- slightly different value to TWH08). A detailed spectroscopic anal- els, and literature results is good (Table A2). ysis is urgently needed. The error budgets calculated by JKTABSDIM tell a similar The physical properties listed in Table 11 (see also Table A5) story to that of TrES-1. The exceptions are that KA is measured show a generally good agreement both internally (except for the £ Fe ¤ more accurately for TrES-2, and a more precise value for H Siess or mass–radius approaches) and with literature studies. The would be the best way to improve knowledge of the properties of values are comparatively imprecise, and improved spectroscopic £ Fe ¤ the system. parameters (KA, Teff, H ) and photometry are required to improve this. New data have been obtained but not yet published (Hrudkova´ et al. 2008). The age of the system is unconstrained by the present 3.3 XO-1 data, so WASP-2 could be anywhere between 0 and 12 Gyr old. XO-1 was the first TEP discovered by the XO survey (McCul- lough et al. 2006) and contains a star with properties very simi- 3.6 HAT-P-1 lar to those of the Sun. The photometric analysis in Paper I was This system was the first TEP discovered by the HAT survey performed using the R- and Z-band light curves presented by Hol- £ Fe ¤ (Bakos et al. 2007a) and excellent light curves have been put for- man et al. (2006). The very low uncertainties in the Teff and H ward by Winn et al. (2007c). The analysis of these data (Paper I) has quoted by McCullough et al. (2006) have been increased to 50 K cemented the position of HAT-P-1 as one of the best-understood and ±0.05 dex here. TEPs, with fractional component radii measured to 3%. The stellar The properties of the star in XO-1 are very close to those of properties are also well-known (Bakos et al. 2007a). the Sun, meaning that all the stellar models (which were calibrated The physical properties of HAT-P-1 in Table 12 are all in rea- on the Sun) agree well. The physical properties of the system are sonable agreement with each other; those descending from the given in Table 9, and the system seems to be quite young. A com- Padova, Y2 and Claret models in particular are highly compatible. parison to literature results is given in Table A3 and shows a good There is also good agreement with literature values (Table A6). The agreement. Claret models propose a young age of 1.6+1.1 Gyr and other models The error budget indicates that a more precise measurement −1.3 are in agreement. It is noticeable that I find an uncertainty in MA of KA, which is observationally straightforward, would be useful. which is substantially smaller than for all literature determinations; A improved rA determination would also help. in the case of TWH08 this arises from their adoption of even larger £ Fe ¤ uncertainties in Teff and H . The error budget shows that this is a well-understood TEP. 3.4 WASP-1 Whilst improvements could be made to the light and velocity WASP-1 was discovered by the SuperWASP consortium (Collier curves, other systems would benefit more from a contribution of Cameron et al. 2007) and decent light curves have been obtained by telescope time. Shporer et al. (2007) and Charbonneau et al. (2007). This TEP has a high inclination (low impact factor), which means that solutions 3.7 OGLE-TR-10 of its light curve are quite degenerate. In Paper I the Shporer and We now leave the realm of bright and easy-to-study TEPs. The Charbonneau data were analysed but yielded measurements of rA OGLE systems have many interesting features but are much more and rb to only 5% accuracy. The asymmetric errorbars from this analysis have been explicitly carried through the analysis presented challenging to observe, due mainly to their faintness and locations here, and the measured physical properties of the system are given in crowded fields. OGLE-TR-10 (Udalski et al. 2002c; Konacki in Table 10. et al. 2003b) is good example of this: the planet is of much in- The Padova and Cambridge 2000 models do not go to a high terest due to its very low density, but it has not yet been possible enough metal abundance (Z = 0.03) so have not been used. Calcu- to obtain definitive light curves or spectroscopy of the system. In lations using the Siess, Y2 and Claret models agree well, and find Paper I I studied two sets of photometry: Magellan observations ages in the region of 3 Gyr. Physical properties calculated using from Holman et al. (2007a) and VLT data from Pont et al. (2007). the mass–radius relation are in poor agreement. Literature results, The Magellan light curves are marred by a systematic underestima- however, are in accord with the results presented here (Table A4). tion of the eclipse depth arising from the use of image-subtraction The error budget indicates that better light and radial velocity photometry (Pont et al. 2007). The VLT data are reliable but unfor- curves are needed to improve measurements of the physical proper- tunately sparse and cover only half of one transit. Here I adopt the ties of WASP-1. Analyses involving more sets of models with high results from Paper I for the VLT V-band and R-band photometry metal abundances will also be useful. obtained by Pont et al. (2007). The high metal abundance of OGLE-TR-10 (Santos et al. 2006) means that the Cambridge 2000 and Padova models could not be used. Results via the Siess, Y2 and Claret models are in 3.5 WASP-2 good agreement with each other (Table 13) and with the literature WASP-2 was discovered by Collier Cameron et al. (2007), and a (Table A7), but all results have large uncertainties due to the limited good z-band light curve was obtained by Charbonneau et al. (2007) observational data available. OGLE-TR-10 b is one of the lowest- and modelled in Paper I. In contrast to WASP-1, the relatively low density planets known. The error budget suggests that good light

°c 0000 RAS, MNRAS 000, 000–000 Homogeneous studies of transiting extrasolar planets. II. 11

−2 Table 9. Derived physical properties for XO-1. In every case gb = 15.8 ± 1.5 m s and ρA = 1.242 ± 0.080ρ¯.

Mass–radius Padova models Siess models Y2 models Cambridge 2007 Claret models

a (AU) 0.0465 ± 0.0013 0.04909 ± 0.00026 0.05002 ∗ ± 0.00035 0.04929 ± 0.00023 0.04909 ± 0.00031 0.04990 ± 0.00029 ∗ MA (M¯) 0.863 ± 0.072 1.015 ± 0.016 1.074 ± 0.023 1.028 ± 0.015 1.015 ± 0.019 1.066 ± 0.018 ∗ RA (R¯) 0.886 ± 0.037 0.935 ± 0.025 0.953 ± 0.027 0.939 ± 0.024 0.935 ± 0.025 0.950 ± 0.022 ∗ loggA (cgs) 4.480 ± 0.018 4.503 ± 0.016 4.511 ± 0.016 4.505 ± 0.017 4.503 ± 0.016 4.510 ± 0.018 ∗ Mb (MJup) 0.818 ± 0.078 0.911 ± 0.071 0.946 ± 0.075 0.918 ± 0.072 0.911 ± 0.072 0.941 ± 0.074 ∗ Rb (RJup) 1.135 ± 0.046 1.198 ± 0.037 1.220 ± 0.038 1.203 ± 0.037 1.198 ± 0.037 1.218 ± 0.038 ∗ ρb (ρJup) 0.559 ± 0.068 0.530 ± 0.063 0.520 ± 0.062 0.528 ± 0.063 0.530 ± 0.063 0.521 ± 0.062 +0.1 ∗ +0.2 +0.7 +0.2 +1.3 Age (Gyr) 0.6−0.0 0.1 −0.0 1.4−1.3 0.3−0.1 0.1−0.0

+1.6 −2 +0.069 Table 10. Derived physical properties for WASP-1. In each case gb = 10.0−1.2 m s and ρA = 0.403−0.037 ρ¯.

Mass–radius Siess models Y2 models Cambridge 2007 Claret models

+0.0011 +0.00040 +0.00037 +0.00035 +0.00031 a (AU) 0.0417−0.0014 0.03955−0.00044 0.03944−0.00044 0.03815−0.00047 0.03933−0.00032 +0.11 +0.040 +0.037 +0.033 +0.031 MA (M¯) 1.52−0.12 1.299−0.043 1.288−0.043 1.166−0.043 1.278−0.031 +0.08 +0.060 +0.056 +0.054 +0.055 RA (R¯) 1.56−0.12 1.477−0.082 1.473−0.086 1.424−0.083 1.469−0.083 +0.035 +0.044 +0.043 +0.043 +0.044 loggA (cgs) 4.236−0.023 4.213−0.026 4.212−0.027 4.197−0.027 4.211−0.026 +0.11 +0.090 +0.089 +0.083 +0.088 Mb (MJup) 1.02−0.12 0.917−0.090 0.912−0.090 0.853−0.084 0.907−0.088 +0.07 +0.060 +0.060 +0.057 +0.059 Rb (RJup) 1.59−0.11 1.506−0.093 1.502−0.092 1.453−0.089 1.498−0.091 +0.058 +0.061 +0.061 +0.063 +0.061 ρb (ρJup) 0.255−0.037 0.268−0.039 0.269−0.039 0.278−0.040 0.270−0.039 +0.4 +0.4 Age (Gyr) 2.7−0.6 2.8 ± 0.5 2.9 ± 0.4 3.1−0.5

−2 Table 11. Derived physical properties for WASP-2. In every case gb = 19.7 ± 2.7 m s and ρA = 1.50 ± 0.21ρ¯.

Mass–radius Padova models Siess models Y2 models Cambridge 2007 Claret models

a (AU) 0.0301 ± 0.0011 0.0309 ± 0.0013 0.0321 ± 0.0010 0.0310 ± 0.0011 0.0312 ± 0.0009 0.0312 ± 0.0013

MA (M¯) 0.784 ± 0.085 0.846 ± 0.110 0.951 ± 0.089 0.858 ± 0.090 0.877 ± 0.078 0.875 ± 0.109 RA (R¯) 0.805 ± 0.061 0.852 ± 0.044 0.859 ± 0.046 0.830 ± 0.044 0.836 ± 0.042 0.835 ± 0.045 loggA (cgs) 4.520 ± 0.032 4.531 ± 0.050 4.548 ± 0.044 4.534 ± 0.046 4.537 ± 0.045 4.536 ± 0.049

Mb (MJup) 0.841 ± 0.085 0.885 ± 0.100 0.956 ± 0.094 0.893 ± 0.089 0.906 ± 0.084 0.905 ± 0.099 Rb (RJup) 1.030 ± 0.069 1.056 ± 0.076 1.098 ± 0.073 1.061 ± 0.071 1.069 ± 0.069 1.068 ± 0.075 ρb (ρJup) 0.77 ± 0.15 0.75 ± 0.14 0.72 ± 0.14 0.75 ± 0.14 0.74 ± 0.14 0.74 ± 0.14

−2 Table 12. Derived physical properties of the HAT-P-1 system. In each case gb = 9.05 ± 0.66 m s and ρA = 0.837 ± 0.076ρ¯.

Mass–radius Padova models Siess models Y2 models Cambridge 2007 Claret models

a (AU) 0.05401 ± 0.00149 0.05540 ± 0.00038 0.05669 ± 0.00033 0.05529 ± 0.00043 0.05464 ± 0.00050 0.05570 ± 0.00049

MA (M¯) 1.054 ± 0.087 1.137 ± 0.023 1.218 ± 0.021 1.130 ± 0.026 1.091 ± 0.030 1.156 ± 0.030 RA (R¯) 1.080 ± 0.055 1.107 ± 0.034 1.133 ± 0.040 1.105 ± 0.034 1.092 ± 0.032 1.113 ± 0.032 loggA (cgs) 4.394 ± 0.022 4.405 ± 0.026 4.415 ± 0.024 4.404 ± 0.026 4.399 ± 0.027 4.408 ± 0.027

Mb (MJup) 0.507 ± 0.033 0.533 ± 0.020 0.558 ± 0.021 0.531 ± 0.020 0.519 ± 0.020 0.539 ± 0.021 Rb (RJup) 1.179 ± 0.049 1.209 ± 0.039 1.237 ± 0.040 1.207 ± 0.039 1.192 ± 0.039 1.216 ± 0.040 ρb (ρJup) 0.309 ± 0.033 0.302 ± 0.031 0.295 ± 0.030 0.302 ± 0.031 0.306 ± 0.031 0.300 ± 0.031 +1.4 +0.4 +0.8 +1.5 +1.1 Age (Gyr) 0.7−1.0 0.1−0.0 2.1−1.0 1.1−1.1 1.6−1.3

°c 0000 RAS, MNRAS 000, 000–000 12 John Southworth

−2 Table 13. Physical properties of the OGLE-TR-10 system. In every case gb = 10.2 ± 2.7 m s and ρA = 0.59 ± 0.11ρ¯.

Mass–radius Siess models Y2 models Cambridge 2007 Claret models

a (AU) 0.0449 ± 0.0017 0.04464 ± 0.00051 0.04476 ± 0.00064 0.04278 ± 0.00071 0.04471 ± 0.00059

MA (M¯) 1.256 ± 0.141 1.233 ± 0.042 1.243 ± 0.053 1.085 ± 0.054 1.239 ± 0.049 RA (R¯) 1.286 ± 0.121 1.278 ± 0.079 1.281 ± 0.086 1.225 ± 0.082 1.280 ± 0.082 loggA (cgs) 4.319 ± 0.041 4.316 ± 0.053 4.317 ± 0.051 4.297 ± 0.052 4.317 ± 0.053

Mb (MJup) 0.67 ± 0.15 0.66 ± 0.14 0.67 ± 0.14 0.61 ± 0.13 0.66 ± 0.14 Rb (RJup) 1.28 ± 0.11 1.27 ± 0.10 1.27 ± 0.10 1.22 ± 0.10 1.27 ± 0.10 ρb (ρJup) 0.32 ± 0.11 0.32 ± 0.11 0.32 ± 0.11 0.34 ± 0.11 0.32 ± 0.11 +1.2 +1.2 +1.5 Age (Gyr) 2.0−1.5 2.0 ± 1.1 2.6−1.1 2.0−1.4 curve are urgently needed, as are more extensive velocity observa- photometry would be useful but of a lower priority than new veloc- tions and a more precise spectral synthesis study. In light of this, ity measurements. OGLE-TR-10 cannot be allowed onto the list of well-understood planetary systems. 3.10 OGLE-TR-132 OGLE-TR-132 was discovered by Udalski et al. (2003) and its 3.8 OGLE-TR-56 planetary nature was confirmed by Bouchy et al. (2004). Its high £ Fe ¤ Similarly to OGLE-TR-10, OGLE-TR-56 (Udalski et al. 2002b; metal abundance ( H = 0.37 ± 0.07; Gillon et al. 2007c) means Konacki et al. 2003a) has only sparse V- and R-band photometry that only the Y2, Cambridge 2007 and Claret models could be used from the VLT (Pont et al. 2007), but in this case the data cover a here. The photometric solution from Paper I was based on the VLT full transit and therefore yield more useful results. Using the photo- light curve of Gillon et al. (2007c). metric solution from Paper I, the physical properties from the mass– The physical properties calculated using the Y2 and Claret radius relation, Siess, Y2 and Claret models (Table 14) agree well models (Table 16) are in good accord and indicate a slightly low with each other and with the independent analysis of TWH08. Pub- stellar surface gravity (loggA = 4.277 ± 0.080). This low gravity lished results are collected in Table A8. is a bit different to those found from spectral synthesis analyses The error budget shows that OGLE-TR-56 would benefit from (loggA = 4.86±0.50, Bouchy et al. 2004; 4.51±0.27, Gillon et al. £ Fe ¤ further observations of all types, particularly more extensive pho- 2007c), indicating that the Teffs and H s measured by these anal- tometry. However, the faintness of OGLE-TR-56 and the extreme yses may be biased. Literature results (Table A10) are in agreement field crowding it suffers from argue in favour of using such tele- with the physical properties presented here. scope time on brighter and less complicated TEPs. Aside from the need for a new spectral synthesis analysis, OGLE-TR-132 would also benefit from additional photometry (covering all of the transit) and particularly velocity measurements. 3.9 OGLE-TR-111 OGLE-TR-111 was detected in a survey towards the Carina con- 3.11 GJ 436 stellation (Udalski et al. 2002a; Pont et al. 2004) rather than the Galactic centre, so suffers from less field crowding than OGLEs GJ 436 is the most important of the known TEPs as it contains the TR-10 and TR-56. It consequently has better photometry (from smallest and least massive planet and star. The eccentric orbit of Winn et al. 2007a), although its faintness means that KA is not the system is also a surprise as tidal effects are expected to have known precisely. In Paper I I presented a solution of the Winn circularised a binary system with such a short orbital period. This et al. (2007a) light curve, which is used here. The spectral synthesis and additional phenomena mean that GJ 436 is a candidate for a £ Fe ¤ study of Santos et al. (2006) found Teff = 5044 ± 83 K and H = multiple-planet system (Ribas et al. 2008a), but the possible prop- 0.19 ± 0.07, in disagreement (3.1σ) with the Teff = 4650 ± 95 K erties of a putative third planet are the subject of intense discussion given by Gallardo et al. (2005). I have adopted the former results (Bean & Seifahrt 2008; Alonso et al. 2008; Ribas et al. 2008b). In £ Fe ¤ as these include a determination of H . A new spectral analysis the current analysis I followed Paper I in adopting an orbital eccen- study is needed to investigate this discrepancy and show which re- tricity of e = 0.14 ± 0.01 (Demory et al. 2007). sults are reliable. The main limitation in our understanding of GJ 436 is our £ Fe ¤ The physical properties of OGLE-TR-111 (Table 15) from us- knowledge of the stellar Teff and H , quantities which are noto- ing the Padova, Siess, Y2 and Claret models agree internally and riously difficult to measure for M dwarfs (e.g. Bonfils et al. 2005). with literature values (Table A9). The Claret models yield an age Adopting the photometric solution from Paper I, I find good agree- +5.4 of 11.5−7.0 Gyr – the poor precision of this value comes from the ment between the Padova, Siess and Claret models for the phys- 2 very long evolutionary timescales of 0.8M¯ stars. If the lower Teff ical properties of the TEP (Table 17). Using the Y models gives from Gallardo et al. (2005) is adopted, the masses and radii of a lower MA and thus RA, Mb and Rb, due to the slightly larger 2 both star and planet decrease by approximately 5% and the age stellar radius for a 0.5M¯ star in these models. The Y results becomes even larger. Either way, OGLE-TR-111 b is one of the are in decent agreement with literature studies (Table A11), most lowest-density planets known. of which used these models in their analysis. Torres (2007) also Aside from the need for a third spectral synthesis analysis, a found a more massive star in one of his solutions, but discounted it more precise value for KA is needed for OGLE-TR-111. Additional due to a poorer agreement with the Hipparcos parallax of GJ 436.

°c 0000 RAS, MNRAS 000, 000–000 Homogeneous studies of transiting extrasolar planets. II. 13

−2 Table 14. Physical properties for OGLE-TR-56. In each case gb = 22.3 ± 7.0 m s and ρA = 0.62 ± 0.21ρ¯.

Mass–radius Siess models Y2 models Cambridge 2007 Claret models

a (AU) 0.02381 ± 0.00137 0.02407 ± 0.00030 0.02390 ± 0.00034 0.02303 ± 0.00031 0.02395 ± 0.00029

MA (M¯) 1.225 ± 0.212 1.266 ± 0.047 1.238 ± 0.053 1.108 ± 0.045 1.247 ± 0.045 RA (R¯) 1.294 ± 0.201 1.268 ± 0.144 1.258 ± 0.148 1.213 ± 0.139 1.261 ± 0.140 loggA (cgs) 4.330 ± 0.070 4.334 ± 0.089 4.331 ± 0.088 4.315 ± 0.089 4.332 ± 0.089

Mb (MJup) 1.29 ± 0.18 1.32 ± 0.14 1.30 ± 0.14 1.21 ± 0.13 1.31 ± 0.14 Rb (RJup) 1.20 ± 0.18 1.21 ± 0.17 1.21 ± 0.17 1.16 ± 0.17 1.21 ± 0.17 ρb (ρJup) 0.75 ± 0.35 0.74 ± 0.34 0.74 ± 0.35 0.77 ± 0.36 0.74 ± 0.35 +1.4 +0.9 +0.8 +1.3 Age (Gyr) 1.2−1.2 1.8−1.4 2.0−2.0 1.6−1.5

−2 Table 15. Derived properties of the OGLE-TR-111 system. In every case gb = 11.5 ± 2.5 m s and ρA = 1.40 ± 0.19ρ¯.

Mass–radius Padova models Siess models Y2 models Cambridge 2007 Claret models

a (AU) 0.04616 ± 0.00162 0.04650 ± 0.00112 0.04745 ± 0.00088 0.04676 ± 0.00067 0.04511 ± 0.00077 0.04702 ± 0.00073

MA (M¯) 0.814 ± 0.085 0.832 ± 0.060 0.884 ± 0.049 0.846 ± 0.036 0.760 ± 0.039 0.860 ± 0.040 RA (R¯) 0.835 ± 0.061 0.842 ± 0.035 0.859 ± 0.038 0.846 ± 0.037 0.816 ± 0.043 0.851 ± 0.032 loggA (cgs) 4.505 ± 0.031 4.508 ± 0.045 4.517 ± 0.042 4.510 ± 0.041 4.495 ± 0.037 4.513 ± 0.044

Mb (MJup) 0.532 ± 0.103 0.540 ± 0.100 0.562 ± 0.103 0.546 ± 0.099 0.508 ± 0.093 0.552 ± 0.101 Rb (RJup) 1.069 ± 0.075 1.077 ± 0.070 1.099 ± 0.070 1.083 ± 0.067 1.045 ± 0.066 1.089 ± 0.068 ρb (ρJup) 0.44 ± 0.11 0.44 ± 0.11 0.52 ± 0.14 0.43 ± 0.11 0.45 ± 0.11 0.43 ± 0.11 +9.9 +3.4 +4.2 +2.0 +5.4 Age (Gyr) 10.8−7.9 10.0−8.8 9.9−4.4 14.3−6.2 11.5−7.0

Given this, the physical properties found using the empirical mass– terminations and exacerbates the anomaly mentioned above. How- radius relation may be closest to the truth, as they return a low mass ever, this result should be treated with caution until improved light of MA = 0.429M¯. However, I retain the results using the Claret curves are included in the analysis. The other types of data for this models for consistency with the rest of the analysis in this work. system are all of definitive quality. The age is unconstrained because 0.5M¯ stars exhibit negligible evolutionary effects in a Hubble time. Further photometry of GJ 436 has become available since pub- 3.13 HD 189733 lication of Paper I, so revised properties of GJ 436 will be presented in the future. There seems no need to obtain further light or velocity As the joint-brightest of the TEPs with HD 209458, HD 189733 curves, but improvements are required to our understanding of the (Bouchy et al. 2005b) has been very well studied. The analysis in spectral characteristics of M dwarfs and their dependence on Teff Paper I was based on definitive light curves from Bakos et al. (2006) £ Fe ¤ and H . and Winn et al. (2006), and gives fractional radii to uncertainties of only 3%. A note of caution is needed here: the solutions of the different passbands did not agree very well, with the scatter being worst for the ratio of the component radii (6.7σ). This is either 3.12 HD 149026 due to systematic errors in the light curves which are not directly HD 149026 b (Sato et al. 2005) is an anomalous TEP because the detectable, or to the presence of starspots. This discrepancy is taken density of the planet is much larger than expected for its mass, sug- into account in the errorbars quoted in Paper I. gesting that much of its matter consists of a rock/ice core. Its bright- HD 189733 appears to be a very young system (0–3 Gyr), and ness temperature, measured through occultation observations at the physical properties presented in Table 19 are in some cases af- 8 µm, is also much greater than we would expect it to be (Harring- fected by the lack of availability of theoretical stellar models for ton et al. 2007). The very shallow transit exhibited by HD 149026 negative ages. Only the Y2 models predict an age greater than the means its photometric parameters are not well known – in Paper I minimum allowed value, so in this respect they are slightly dis- ◦ I found an inclination of i ≈ 90 which is quite different to other crepant. If the Teff is lowered by 1σ this difficulty disappears, in- determinations. This solution, which has since been supported by dicating that it has not caused a major problem in the resulting Winn et al. (2008a), leads to a smaller star and planet compared to properties. The uncertainties on individual sets of physical prop- previous measurements. I adopt this solution here. erties are definitely affected by these edge effects, but this does The physical properties of HD 149026 from the Y2 and Claret not wrap into the final values (see Section 5) as the largest uncer- models (Table 18) are quite different to all previous studies expect tainties are always adopted (in this case from the Y2 model solu- that of TWH08, who also found a high-inclination light curve so- tions). Given these problems, it is reassuring that all studies have lution. A comparison with the results of Sato et al. (2005); Char- found similar values for the physical properties of the HD 189733 bonneau et al. (2006); Wolf et al. (2007); Winn et al. (2008a) and system (Table A13; Bouchy et al. 2005b; Bakos et al. 2006; Winn TWH08 is made in Table A12. I consequently find a planetary den- et al. 2006, 2007b; Torres et al. 2008. As an additional check, +0.71 sity of ρb = 1.56−0.57 ρJup which is the highest of all published de- the interferometrically-measured stellar radius of RA = 0.779 ±

°c 0000 RAS, MNRAS 000, 000–000 14 John Southworth

−2 Table 16. Derived properties of the OGLE-TR-132 system. In all cases gb = 15.6 ± 6.1 m s and ρA = 0.50 ± 0.15ρ¯.

Mass–radius Y2 models Cambridge 2007 models Claret models

a (AU) 0.03081 ± 0.00160 0.03050 ± 0.00034 0.02879 ± 0.00044 0.03040 ± 0.00033

MA (M¯) 1.365 ± 0.213 1.325 ± 0.044 1.114 ± 0.051 1.311 ± 0.043 RA (R¯) 1.397 ± 0.201 1.38 ± 0.14 1.31 ± 0.14 1.38 ± 0.14 loggA (cgs) 4.283 ± 0.062 4.278 ± 0.079 4.253 ± 0.079 4.277 ± 0.079

Mb (MJup) 1.02 ± 0.32 1.00 ± 0.30 0.89 ± 0.27 1.00 ± 0.30 Rb (RJup) 1.28 ± 0.17 1.26 ± 0.15 1.19 ± 0.15 1.26 ± 0.15 ρb (ρJup) 0.49 ± 0.24 0.50 ± 0.24 0.53 ± 0.26 0.50 ± 0.24 +0.6 +0.5 +0.6 Age (Gyr) 1.4−1.1 1.9−1.3 1.5−1.4

−2 Table 17. Derived properties of the GJ 436 TEP system. In each case gb = 13.7 ± 1.1 m s and ρA = 4.92 ± 0.55ρ¯.

Mass–radius Padova models Siess models Y2 models Claret models

a (AU) 0.0282 ± 0.0013 0.02928 ± 0.00070 0.02995 ± 0.00042 0.02882 ± 0.00066 0.02972 ± 0.0010

MA (M¯) 0.429 ± 0.060 0.479 ± 0.035 0.513 ± 0.022 0.457 ± 0.031 0.501 ± 0.053 RA (R¯) 0.443 ± 0.031 0.460 ± 0.026 0.471 ± 0.023 0.453 ± 0.021 0.467 ± 0.025 loggA (cgs) 4.777 ± 0.031 4.793 ± 0.025 4.803 ± 0.027 4.786 ± 0.032 4.799 ± 0.034

Mb (MJup) 0.0704 ± 0.0069 0.0757 ± 0.0042 0.0793 ± 0.0032 0.0734 ± 0.0039 0.0781 ± 0.0059 Rb (RJup) 0.357 ± 0.022 0.371 ± 0.017 0.379 ± 0.015 0.365 ± 0.016 0.376 ± 0.019 ρb (ρJup) 1.54 ± 0.20 1.49 ± 0.18 1.45 ± 0.17 1.51 ± 0.18 1.47 ± 0.18

+6.8 −2 +0.08 Table 18. Physical properties of the HD 149026 system. In all cases gb = 23.7−6.2 m s and ρA = 0.59−0.13 ρ¯.

Mass–radius Y2 models Cambridge 2007 models Claret models

−2 Table 19. Derived physical properties of HD 189733. In every case gb = 22.0 ± 1.4 m s and ρA = 1.98 ± 0.16ρ¯.

Mass–radius Padova models Siess models Y2 models Cambridge 2007 Claret models

a (AU) 0.02932 ± 0.00097 0.03129 ± 0.00019 0.03189∗ ± 0.00024 0.03122 ± 0.00036 0.03144 ± 0.00021 0.03175∗ ± 0.00019 ∗ ∗ MA (M¯) 0.682 ± 0.067 0.830 ± 0.016 0.878 ± 0.020 0.824 ± 0.029 0.841 ± 0.017 0.866 ± 0.015 ∗ ∗ RA (R¯) 0.701 ± 0.036 0.749 ± 0.024 0.763 ± 0.027 0.747 ± 0.022 0.752 ± 0.025 0.760 ± 0.022 ∗ ∗ loggA (cgs) 4.580 ± 0.022 4.608 ± 0.023 4.616 ± 0.021 4.607 ± 0.025 4.610 ± 0.022 4.615 ± 0.024 ∗ ∗ Mb (MJup) 1.023 ± 0.074 1.165 ± 0.037 1.210 ± 0.040 1.159 ± 0.043 1.176 ± 0.034 1.199 ± 0.038 ∗ ∗ Rb (RJup) 1.074 ± 0.047 1.146 ± 0.034 1.168 ± 0.035 1.143 ± 0.035 1.151 ± 0.034 1.163 ± 0.034 ∗ ∗ ρb (ρJup) 0.827 ± 0.080 0.774 ± 0.071 0.760 ± 0.069 0.776 ± 0.071 0.771 ± 0.070 0.763 ± 0.069 +2.9 ∗ +0.0 +4.2 ∗ +0.0 +3.3 Age (Gyr) 0.1−0.0 0.1 −0.0 3.7−4.1 0.1 −0.0 0.1−0.0

°c 0000 RAS, MNRAS 000, 000–000 Homogeneous studies of transiting extrasolar planets. II. 15

0.052R¯ given by Baines et al. (2007) is in good agreement with Table 21. Detailed error budget for the calculation of the system properties the results presented here, with the additional bonus that it is al- of HD 209458 using the Claret (2007) stellar models. The layout of the table most independent of stellar theory. It may be worthwhile to revisit is the same as that for Table 6. the Teff determination for HD 189733, as a slightly lower temperature would obliterate the difﬁculties found above. Output Input parameter £ Fe ¤ parameter KA i rA rb Teff H

3.14 HD 209458 Age 0.074 0.738 0.664 a 0.038 0.685 0.720

In contrast to its position as the last object studied in this work, MA 0.038 0.686 0.720 HD 209458 was the first TEP to be discovered (Charbonneau et al. RA 0.228 0.666 0.701 2000; Henry et al. 2000). This, combined with its bright appar- loggA 0.452 0.610 0.642 ent magnitude, means that the available light curves of HD 209458 ρA 0.001 1.000 0.001 0.001 form a catalogue of observations of remarkable quality. In Paper I I Mb 0.568 0.004 0.031 0.564 0.592 analysed the original HST observations from Brown et al. (2001), Rb 0.029 0.645 0.523 0.550 the stunning ten-band HST data from Knutson et al. (2007), and the gb 0.633 0.004 0.774 high-duty-cycle MOST light curve from Rowe et al. (2006). These ρb 0.452 0.003 0.012 0.829 0.224 0.236 datasets allowed determination of the fractional radii to accuracies of better than 1%, a level which has not been achieved for any other TEP. As with HD 189733, the high quality of these data allowed Table 22. Detailed error budget for the calculation of the system properties the detection of differences between the individual light curves (at of HD 209458 using the empirical mass–radius relation. The layout of the the 5.6σ level here) which are due either to systematic errors or table is the same as for Table 7. starspots. These discrepancies are accounted for in the errorbars in Paper I. Output Input parameter The results from Paper I have been combined with the KA parameter KA i rA rb MR0 MR1 measured by Naef et al. (2004). There are several spectral syn- a 0.048 0.666 0.744 thesis studies in the literature (Allende Prieto & Lambert 1999; M 0.048 0.665 0.745 Mazeh et al. 2000; Santos et al. 2004) and these are in good agree- A R 0.141 0.660 0.738 ment with each other and with semiempirical results based on in- A loggA 0.140 0.660 0.738 frared photometry (Ribas et al. 2003). I adopt Teff = 6117 ± 50 K ρ 0.001 1.000 0.001 0.002 £ Fe ¤ A and H = 0.02 ± 0.05 from Santos et al. (2004); this study also Mb 0.255 0.002 0.046 0.643 0.720 finds logg = 4.48±0.08. As independent checks, uvbyβ photom- A Rb 0.045 0.307 0.634 0.709 etry and the calibration grids of Moon & Dworetsky (1985) give gb 0.633 0.004 0.774 Teff = 6080 ± 30 K and loggA = 4.26 ± 0.06, and a preliminary ρb 0.354 0.002 0.032 0.650 0.448 0.500 analysis using the Infrared Flux Method (Blackwell & Shallis 1977; Blackwell et al. 1980) yields Teff = 6180 ± 220 K (Dr. B. Smalley, private communication). properties are those from the calculations involving the Claret the- The resulting physical properties (Table 20) are very well con- oretical models. Each quantity has a quoted statistical uncertainty, strained, and in good agreement with most literature studies (Ta- which arises from the propagation of errors in all input parameters ble A14). £ ¤ (P , i, r , r , K , T and Fe ). For the statistical uncertainty of A detailed error budget for the calculations using the Claret orb A b A eff H each quantity I quote (slightly conservatively) the largest of the un- models is given in Table 21, and shows that most of the uncertainty certainties found from calculations involving the three model sets in the physical parameters comes from the uncertainties in the Teff £ ¤ which show good interagreement (Claret, Padova and Y2). and Fe measurements. As these are realistically limited to mini- H Every calculated physical property also has a quoted system- mum values of ±50 K and ±0.05 dex, respectively, due to our un- atic uncertainty, which comes from the variation in physical proper- derstanding of the temperature scale of low-mass stars, there is no ties between calculations using these three sets of theoretical mod- immediate hope of improvement. The planetary properties are still els. These systematic uncertainties are lower limits on the true sys- mainly dependent on the input K and r – both of these values A b tematics, because the different model sets have many similarities in are already known to very high precision and would require much their calculation methods (see Section 2.1.1. The systematic uncer- work to improve. The analysis here therefore results in quantities tainties depend on calculations involving only three sets of stellar which are highly reliable and unlikely to change in the near future. models; additional model sets will be added in the future to im- HD 209458 is the best-understood extrasolar planetary system. The prove the precision. For four systems (OGLE-TR-10, OGLE-TR- error budget for calculations using the empirical mass–radius rela- 56, OGLE-TR-132 and HD 149026) the Padova models did not ex- tion (Table 22) confirms these conclusions. £ Fe ¤ tend to a high enough H so the systematic uncertainty estimates are based on only the Y2 and Claret models. Systematic uncertainties are not quoted for gb or ρA as these quantities have, respec- 4 PHYSICAL PROPERTIES OF THE TRANSITING tively, zero and negligible dependence on theoretical calculations. EXTRASOLAR PLANETARY SYSTEMS In most cases, the lower limits on the systematic errors are quite a bit smaller than the statistical ones. This is the situation for 4.1 Using stellar models all the planetary properties (Mb, Rb, gb, ρb), which means that they The final model-dependent physical properties of the TEPs studied should be reliably determinable observationally. The two quanti- in this work are collected in Tables 23 and 24. The values of the ties for which model-dependent systematics are important are the

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−2 Table 20. Derived properties of the HD 209458 system. In all cases gb = 9.08 ± 0.17 m s and ρA = 0.727 ± 0.005ρ¯.

Mass–radius Padova models Siess models Y2 models Cambridge 2007 Claret models

a (AU) 0.04724 ± 0.00105 0.04742 ± 0.00045 0.04888 ± 0.00032 0.04757 ± 0.00034 0.04799 ± 0.00029 0.04770 ± 0.00041

MA (M¯) 1.132 ± 0.076 1.144 ± 0.033 1.253 ± 0.025 1.155 ± 0.025 1.186 ± 0.021 1.165 ± 0.030 RA (R¯) 1.159 ± 0.026 1.163 ± 0.011 1.199 ± 0.008 1.167 ± 0.009 1.177 ± 0.008 1.170 ± 0.010 loggA (cgs) 4.364 ± 0.010 4.365 ± 0.005 4.378 ± 0.003 4.367 ± 0.004 4.370 ± 0.003 4.368 ± 0.004

Mb (MJup) 0.693 ± 0.032 0.698 ± 0.016 0.742 ± 0.013 0.703 ± 0.013 0.715 ± 0.012 0.707 ± 0.015 Rb (RJup) 1.376 ± 0.032 1.381 ± 0.016 1.424 ± 0.014 1.386 ± 0.014 1.398 ± 0.013 1.389 ± 0.015 ρb (ρJup) 0.266 ± 0.009 0.265 ± 0.007 0.257 ± 0.007 0.264 ± 0.007 0.262 ± 0.007 0.263 ± 0.007 +0.9 +0.6 +0.6 +0.7 Age (Gyr) 1.7−0.7 0.2−0.1 2.3 ± 0.5 0.5−0.3 2.3−0.6

Table 23. Physical properties of the stellar components of the TEPs studied in this work. For each quantity the ﬁrst uncertainty is derived from a propagation of all observational errors and the second uncertainty is an estimate of the systematic errors arising from the variation between results using different sets of stellar models.

System Mass (M¯) Radius (R¯) loggA [cm/s] Density (ρ¯) Age (Gyr)

+4.1 TrES-1 0.929 ± 0.030 ± 0.037 0.829 ± 0.015 ± 0.011 4.569 ± 0.018 ± 0.006 1.632 ± 0.092 1.2−1.8 ± 2.2 +1.6 TrES-2 0.991 ± 0.050 ± 0.025 0.994 ± 0.031 ± 0.009 4.440 ± 0.028 ± 0.004 1.010 ± 0.092 5.3−2.6 ± 0.8 +1.3 XO-1 1.066 ± 0.018 ± 0.051 0.950 ± 0.025 ± 0.015 4.510 ± 0.018 ± 0.007 1.242 ± 0.080 1.0−0.9 ± 1.5 +0.040 +0.000 +0.060 +0.000 +0.044 +0.000 +0.069 +0.4 WASP-1 1.278 −0.043 −0.021 1.469 −0.086 −0.008 4.211 −0.027 −0.002 0.403 −0.037 3.1−0.5 ± 0.3 WASP-2 0.88 ± 0.11 ± 0.03 0.835 ± 0.045 ± 0.017 4.536 ± 0.050 ± 0.005 1.50 ± 0.21 unconstrained +1.1 HAT-P-1 1.156 ± 0.030 ± 0.026 1.113 ± 0.034 ± 0.008 4.408 ± 0.027 ± 0.004 0.837 ± 0.076 1.6−1.3 ± 0.9 +1.5 OGLE-TR-10 1.239 ± 0.053 ± 0.006 1.280 ± 0.086 ± 0.002 4.317 ± 0.053 ± 0.001 0.590 ± 0.110 2.0−1.4 ± 0.0 +1.3 OGLE-TR-56 1.247 ± 0.053 ± 0.019 1.26 ± 0.15 ± 0.01 4.332 ± 0.089 ± 0.002 0.620 ± 0.210 1.6−1.5 ± 0.2 +5.4 OGLE-TR-111 0.860 ± 0.060 ± 0.028 0.851 ± 0.037 ± 0.009 4.513 ± 0.045 ± 0.005 1.400 ± 0.190 11.5−7.0 ± 1.6 +0.6 OGLE-TR-132 1.311 ± 0.044 ± 0.014 1.38 ± 0.14 ± 0.00 4.277 ± 0.079 ± 0.001 0.50 ± 0.15 1.5−1.4 ± 0.1 GJ 436 0.501 ± 0.053 ± 0.044 0.467 ± 0.026 ± 0.014 4.799 ± 0.034 ± 0.013 4.92 ± 0.55 unconstrained +0.033 +0.000 +0.121 +0.000 +0.039 +0.000 +0.083 HD 149026 1.277 −0.023 −0.008 1.292 −0.058 −0.003 4.321 −0.069 −0.001 0.592 −0.129 1.2 ± 1.0 ± 0.0 HD 189733 0.866 ± 0.029 ± 0.042 0.760 ± 0.024 ± 0.013 4.615 ± 0.025 ± 0.008 1.980 ± 0.170 0.0–3.4 ± 3.6 +0.7 HD 209458 1.165 ± 0.033 ± 0.021 1.170 ± 0.011 ± 0.007 4.368 ± 0.005 ± 0.003 0.727 ± 0.005 2.3−0.6 ± 0.6 orbital semimajor axis and stellar mass: for these the two types of errors are generally of a similar size. Thus a and MA are the two quantities which are least reliably determined. The importance of systematic versus statistical uncertainties is shown in Figures 3 and 4, where statistical uncertainties are shown with black open diamonds and systematic uncertainties with red filled diamonds. In Fig. 3 it can be seen that the systematic uncertainties are important for only a minority of TEPs, but that in these cases can be substantially larger than the statistical ones. It is noticeable that the stars do not follow the empirical mass–radius relation (Eq. 2), which is expected because their properties have been determined using stellar models which also do not reproduce this relation. At larger masses the stars have disproportionately larger radii, suggesting that they are slightly evolved. There are two reasons why the known population of TEPs may be biased in favour of slightly evolved stars. Firstly, they are larger and so a given planet is more likely to be transiting. Secondly, they are brighter so will be over-represented in the magnitude-limited samples which are studied to find TEPs. For more evolved stars, planetary transits will Figure 3. Plot of the masses versus the radii of the stars in the fourteen be shallower and more difficult to detect, so these will be under- TEPs studied in this work. The statistical uncertainties are shown by black represented in observational populations of TEPs. open diamonds and the systematic uncertainties by red filled diamonds. The Fig. 4 shows that systematic uncertainties are generally unim- empirical mass–radius relation derived in Section 2.2) is shown with a blue portant compared to statistical uncertainties for the planetary mass unbroken line. and radius measurements, but that they are significant in some cases. The systems which are most affected are GJ 436, whose low-

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Table 24. Physical properties of the planetary components of the TEPs studied in this work. For each quantity the ﬁrst uncertainty is derived from a propagation of all observational errors and the second uncertainty is an estimate of the systematic errors arising from the variation between results using different sets of stellar models.

−2 System Semimajor axis (AU) Mass (MJup) Radius (RJup) Gravity ( m s ) Density (ρJup) TrES-1 b 0.04000 ± 0.00043 ± 0.00054 0.781 ± 0.045 ± 0.021 1.114 ± 0.032 ± 0.015 15.6 ± 1.2 0.565 ± 0.055 ± 0.008 TrES-2 b 0.03568 ± 0.00061 ± 0.00031 1.206 ± 0.045 ± 0.020 1.226 ± 0.040 ± 0.010 19.9 ± 1.2 0.654 ± 0.057 ± 0.006 XO-1 b 0.04990 ± 0.00029 ± 0.00081 0.941 ± 0.074 ± 0.030 1.218 ± 0.038 ± 0.020 15.8 ± 1.5 0.521 ± 0.063 ± 0.009 +0.00040 +0.00000 +0.090 +0.000 +0.060 +0.000 +1.6 +0.061 +0.002 WASP-1b 0.03933 −0.00044 −0.00022 0.907 −0.090 −0.010 1.498 −0.093 −0.008 10.0 −1.2 0.270 −0.039 −0.000 WASP-2b 0.03120 ± 0.00130 ± 0.00030 0.91 ± 0.10 ± 0.02 1.068 ± 0.076 ± 0.012 19.7 ± 2.7 0.74 ± 0.14 ± 0.01 HAT-P-1 b 0.05570 ± 0.00049 ± 0.00041 0.539 ± 0.021 ± 0.008 1.216 ± 0.040 ± 0.009 9.05 ± 0.66 0.300 ± 0.031 ± 0.002 OGLE-TR-10 b 0.04471 ± 0.00064 ± 0.00007 0.66 ± 0.14 ± 0.01 1.27 ± 0.10 ± 0.00 10.1 ± 2.7 0.32 ± 0.11 ± 0.00 OGLE-TR-56 b 0.02395 ± 0.00034 ± 0.00012 1.31 ± 0.14 ± 0.01 1.21 ± 0.17 ± 0.00 22.3 ± 7.0 0.74 ± 0.35 ± 0.00 OGLE-TR-111 b 0.0470 ± 0.0011 ± 0.0005 0.55 ± 0.10 ± 0.01 1.089 ± 0.070 ± 0.012 11.5 ± 2.5 0.43 ± 0.11 ± 0.01 OGLE-TR-132 b 0.03040 ± 0.00034 ± 0.00010 1.00 ± 0.30 ± 0.00 1.26 ± 0.15 ± 0.00 15.6 ± 6.1 0.50 ± 0.24 ± 0.00 GJ 436 b 0.0297 ± 0.0010 ± 0.0009 0.078 ± 0.005 ± 0.004 0.376 ± 0.019 ± 0.011 13.7 ± 1.1 1.47 ± 0.18 ± 0.04 +0.00037 +0.00000 +0.012 +0.000 +0.099 +0.000 +6.8 +0.71 +0.00 HD 149026 b 0.04294 −0.00026 −0.00009 0.357 −0.011 −0.001 0.611 −0.072 −0.001 23.7 −6.2 1.56 −0.57 −0.00 HD 189733 b 0.03175 ± 0.00036 ± 0.00053 1.199 ± 0.043 ± 0.040 1.163 ± 0.035 ± 0.020 22.0 ± 1.4 0.763 ± 0.071 ± 0.013 HD 209458 b 0.04770 ± 0.00045 ± 0.00028 0.707 ± 0.016 ± 0.009 1.389 ± 0.016 ± 0.008 9.08 ± 0.17 0.263 ± 0.007 ± 0.002

For completeness the results for each TEP using the mass– radius relation are collected in Tables A15 and A16. In the rest of this work I adopt the physical properties calculated using stellar models. Whether this step is correct is not yet clear, and will not be until we properly understand why theoretical predictions do not match the measured radii of stars in low-mass eclipsing binaries.

4.3 Comparing different methods Fig. 5 contains a comparison between the stellar masses determined in different ways in this work and in TWH08. The comparison has been undertaken using MA because this is the physical property which is most dependent on stellar models or mass–radius relations, so shows differences most clearly. The various sets of physical properties for each TEP come from the same measured quantities; they differ only in the value of Kb adopted to satisfy whichever additional constraint is imposed. The left panels in Fig. 5 compare the final masses against those obtained using the mass–radius relation or one of the three sets of adopted stellar models. The agreement between the masses found Figure 4. Plot of the masses versus the radii of the planets in the fourteen in different ways has been quantified by calculating the mean of TEPs studied in this work. The statistical uncertainties are shown by black the deviations from parity for each comparison. The results from open diamonds and the systematic uncertainties by red filled diamonds. the three model sets agree very well: the mean deviation from the Blue unbroken lines show the loci of constant densities of 0.25, 0.5 and 2 final (Claret) masses is 0.020M¯ for the Y and 0.030M¯ for the 0.5 ρJup (from bottom to top). Padova models. Using the mass–radius relation produces masses which are generally smaller and scattered; the mean deviation here mass star is not well-understood by current theory, and HD 189733, is 0.093M¯. which is a young system. The right panels in Fig. 5 show comparisons with results from the three sets of models which were not used to determine the final masses. The Siess models produce MAs which are a bit larger on average than the baseline results: this is because they tend to predict 4.2 Using the empirical mass–radius relation denser stars than the other model sets (mean deviation 0.036M¯). Use of the empirical mass–radius relation instead of theoretical pre- The Cambridge 2000 models can be applied to the fewest systems dictions yields physical properties which are, generally, smaller. studied here due to their lesser coverage in mass and metallicity, This is most pronounced for the two quantities which are most de- but agree quite well for the eight stars within their remit (mean dependent on outside constraints: MA and a. The values of these can viation 0.029M¯). The Cambridge 2007 models do not agree well diminish by 15% or more compared to calculations involving stel- (mean deviation 0.094M¯) and also show quite a lot of scatter. This lar models (e.g. TrES-1 and XO-1). This effect is less significant for effect seems to depend on metallicity, with the outliers above and the other quantities. The difference is largest for systems with stel- below the line of parity being respectively metal-poor (TrES-2) and lar masses of 0.7–1.1M¯, where the radius discrepancy between metal-rich (HD 149026 and the OGLEs). It should be remembered models and observations is most severe. that the Cambridge models are targeted towards more massive stars,

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Figure 6. Mass–radius plot for the known transiting extrasolar planets. Both axes are logarithmic. The fourteen objects studied in this work are shown with black ﬁlled circles and the remaining ones by grey open circles. The four gas giant planets in our Solar System are denoted with asterisks. Dotted lines show loci of constant density (1.0, 0.5 and 0.25 ρJup, from bottom to top).

5 PROPERTIES OF THE KNOWN TRANSITING EXTRASOLAR PLANETARY SYSTEMS The physical properties of the fourteen TEPs studied in this work have been augmented with results from the refereed literature for the other known TEPs. The overall sample now contains 41 systems, including only those which are the subject of a study in a refereed journal (including pre-publication papers on preprint servers). The properties of the full sample are reproduced in Tables Figure 5. Comparison between the stellar masses determined in different 23 and 24. ways in this work and with TWH08. ‘This work’ refers to the masses in The mass–radius diagram for all known extrasolar planets is Table 23, where the random uncertainties and systematic errors have been reproduced in Fig. 6, and shows a strong clustering of objects in the added in quadrature. In each case parity is shown with a dotted line. As the region of 0.5–1.1MJup and 0.9–1.5RJup. The presence of outliers to ﬁnal masses were derived using the Claret models as a baseline, a compar- larger mass but comparable radius is consistent with expectations ison with these masses shows perfect agreement. The corresponding panel that massive planets, brown dwarfs and low-mass stars have similar has been retained in the plot because the uncertainties in the ﬁnal masses radii (Chabrier & Baraffe 2000; Pont et al. 2005). The planet with include the systematic contribution whereas those derived using only the the largest radius is TrES-4 (Mandushev et al. 2007); it is the only Claret models do not. one to have a density less than a quarter that of Jupiter. The reason why TrES-4 is an outlier remains unclear.

5.1 Correlations with orbital period A correlation between the orbital periods and surface gravities of exoplanets was found by Southworth et al. (2007b) and confirmed in Paper I. The impressive influx of new discoveries in early 2008 and should not be criticized too strongly for possible discrepancies means this possibility can now be investigated on 41 TEPs instead in the mass range of interest here. of the 30 involved in Paper I. The corresponding diagram is plotted Finally, a comparison with the stellar masses found by in Fig. 7. There are three planets which have much higher masses TWH08 (Fig. 5, bottom-right panel) shows decent agreement: all and thus surface gravities: HAT-P-2 b (Mb = 11.8MJup), WASP– MAs agree to within their errors: the mean deviation between the 14 b (7.73MJup) and XO-3 b (11.8MJup). These unusual properties stellar mass values is 0.032M¯. The masses from TWH08 are on mean that they are clear outliers in Fig. 7, so I have discounted them average slightly lower than those found in this work: this system- when assessing the statistical significance of the period–gravity atic effect is not large enough to worry about at present, but may correlation. For this I have used two rank coefficient correlation need attention in the future during statistical analysis of a larger tests: Spearman’s ρ returns a probability of 98.3% and Kendall’s τ sample of TEPs. a probability of 98.9% that this correlation is significant.

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into Class I and Class II in Fig. 9 is not strong. Whilst Class II planets (lower Θ) still tend to group together, the distribution of Class I planets is much more nebulous than has previously been found, and several TEPs now appear to be intermediate between the two classes. The objects which now fill in the previously clear gap are all recent discoveries: HAT-P-5, HAT-P-6, HAT-P-7, OGLE-TR- 211 and WASP-3. Whilst improved observations for these may lower the errorbars and reinstate the divide, on current evidence the separation between Class I and Class II seems to have been a statistical fluke. It should also be stated that the finding that Class II TEPs have generally larger Rb and MA, and smaller Mb, is encour- aged by the definition of the Safronov number (Θ ∝ Mb ). MARb TWH08 found that the division between Class I and Class II was clear in their sample of TEPs, that Class II planets are less massive than Class I ones for a given Teq, and that there is a correlation £ Fe ¤ with the stellar H . Similarly to my finding that the division is less obvious, the data in hand also do not lend strong support to £ Fe ¤ the correlation with H . However, the divide in a plot of Mb versus Teq is clear. Further investigation of these results needs a larger sample of well-studied TEPs. Figure 9. Plot of equilibrium temperature versus Safronov number for the full sample of planets. Those studied in this work are shown with black filled circles and those whose properties are taken from the the literature are shown with grey errorbars. The dotted line represents the divide envisaged 6 SUMMARY AND FUTURE DIRECTIONS by Hansen & Barman (2007). Five planets lie outside this plot towards large The discovery of the first transiting extrasolar planetary system, Safronov numbers: HAT-P-2 b, XO-3 b, WASP-10, WASP-14b, OGLE-TR- HD 209458 (Charbonneau et al. 2000; Henry et al. 2000), opened 113 b and HD 17156 b. The outlying point at the lower left is GJ 436. up a new area of research in stellar and planetary astrophysics. Whilst we had to wait several years for the second TEP to be iden- A correlation of planet mass with orbital period was demon- tified (Konacki et al. 2003a), the ensuing flow of new discoveries strated by Mazeh et al. (2005). The corresponding diagram is plot- has gradually increased to the point where roughly fifty of these ob- ted in Fig. 8, in which the correlation remains discernable. Using jects are known. In the near future we can expect this steady stream the above sample of 41 TEPs with the three high-mass outliers re- to build up to a flood as ground-based searches refine their tech- moved, Spearman’s ρ and Kendall’s τ return probabilities of 96.2% niques, and new planets are discovered by the CoRoT and Kepler and 94.7%, respectively, that this correlation not circumstantial. space missions (Baglin et al. 2006; Basri et al. 2005). It has previously been noticed (Joshi et al. 2008) that the three At present, TEPs are studied using diverse methods, causing planets which do not fit into the period–mass and period–gravity inhomogeneity in the results. This series of papers establishes a single set of methods for the analysis of photometric and spectroscopic relations all have a high mass (9.72, 7.73 and 11.8MJup) and an eccentric orbit (e = 0.52, 0.095 and 0.26). It is also the case that their observations of TEPs. It is aimed at providing homogeneous and robust physical properties for these objects, which can then be stud- parent stars are very similar, with Teffs of 6290, 6475 and 6429 K, ied statistically in order to elicit the maximum information from and masses of 1.31, 1.32 and 1.21 M¯, for HAT-P-2, WASP-14 and XO-3 respectively. This may imply something interesting about the existing observational data. Paper I presented analyses of the light formation of planetary systems, but additional objects are needed curves of the fourteen TEPS for which good data were then avail- before any conclusions are arrived at. able. In this work the analysis is extended, using the predictions of theoretical stellar evolutionary models, to produce the physical properties of the stellar and planetary components of each TEP. 5.2 Safronov numbers Emphasis is placed on understanding the statistical and systematic errors in these quantities. Hansen & Barman (2007) presented evidence that there are two Modelling the light curve of a TEP allows the quantities Porb, classes of extrasolar planet which occupy different regions of a plot i, rA and rb to be measured. Radial velocity measurements con- of equilibrium temperature (T ) versus Safronov (1972) number, eq tribute KA to this mix, leaving us one piece of information short of the square of the ratio of escape velocity to orbital velocity: being able to derive the masses and radii of the two components. In µ ¶2 most cases stellar theory is called upon to provide this missing da- 1 Vesc a M £ ¤ Θ = = b (15) tum by inferring the mass of the star from its measured T , Fe , 2 V R M eff H orb b A and light-curve-derived density. In this work I determine the stellar Hansen & Barman (2007) found that a sample of 19 TEPs divided mass which gives the optimal fit to all of the above measurements, naturally into two classes based on their Safronov number, with the allowing derivation of the physical properties and age of the system split at Θ = 0.05. Those in Class II (Θ ≈ 0.04 ± 0.01) were found which best satisfy these constraints. to have in general smaller planetary mass and larger stellar masses; This process has a clear dependence on stellar theory, which Class II also contains all the planets with anomalously large radii. may cause systematic errors in the derived properties. To estimate The equations given by Hansen & Barman (2007) for Teq and these systematics I have obtained separate solutions, for each of Θ have been used to construct a plot of these quantities, Fig. 9, the fourteen TEPs studied in Paper I, using tabulated predictions which contains 34 TEPs (five are outside the plot). The division from six different sets of stellar models. The results from using

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Figure 7. Plot of the orbital periods versus the surface gravities of all TEPs for which this information is available. Black ﬁlled circles denote the fourteen systems studied in this work and grey open circles represent numbers taken from the literature. The inset panel is an enlarged view of the region occupied by the bulk of the TEPs.

Figure 8. Plot of the orbital periods versus the planetary masses of all known TEPs. The symbols and inset panel are as in Fig. 8.

°c 0000 RAS, MNRAS 000, 000–000 Homogeneous studies of transiting extrasolar planets. II. 21 three of these model sets, Y2, Padova and Claret, are always in significant at the 98–99% level. The related correlation between good agreement. The dispersion between the different results for period and mass for TEPs (Mazeh et al. 2005) is weaker but still the three model sets neatly allows a systematic error to be estimated significant at the 94–95% (2σ) level. Both of these significance as- for every output quantity. sessments were calculated after rejecting three systems (HAT-P-2, The statistical errors have been propagated through the anal- WASP-14 and XO-3) with eccentric orbits, unusually high plane- ysis using a perturbation algorithm, which allows a complete error tary masses, and very similar stellar Teffs. These three systems are budget to be obtained for every output quantity in each calculation. obvious outliers on most plots of the properties of TEPs and may It turns out that the uncertainties in the planetary and stellar radii represent a group of planetary systems which formed in a different are dominated by the statistical uncertainties from the light curve way to most TEPs. Hansen & Barman (2007) found that the known modelling, and that the systematic errors are mostly much smaller. TEPs have a bimodal distribution of Safronov numbers. This divi- The mass of each planet is mainly sensitive to the input KA, which sion into two classes has weakened considerably with the addition is a directly observed quantity. Thus the physical properties of the of newly-discovered TEPs, and may not be statistically significant. transiting planets are reliable as they have only a minor dependence The detailed error budgets calculated for each TEP studied on theoretical calculations. In contrast, the semimajor axis and stel- in this work have allowed an assessment of which object would lar mass are quite sensitive to stellar model predictions, and in some most benefit from what type of follow-up observations. TrES-2, cases the systematic errors are up to three times larger than the sta- WASP-2 and GJ 436 are good targets for new spectral synthesis tistical ones. Therefore several sets of stellar models should always studies. Several systems have only a limited number of radial ve- be used for this kind of analysis, to check for the presence of sys- locity measurements, which are sufficient to confirm their plane- tematic errors. tary nature but are rather inaccurate for determining their physical A major caveat applies to the previous paragraph. Different properties. These include TrES-1, XO-1, WASP-1 and WASP-2; sets of stellar models use much of the same input physics (for exam- they are bright enough that more extensive velocity measurements ple opacities, treatment of convective mixing and calibration using will not require too much effort. Obtaining additional light curves our Sun), so cannot be considered totally independent. Also, only would be a good idea for XO-1 and WASP-1. The four OGLE plan- those models which showed a good mutual agreement were consid- ets studied here (OGLE-TR-10, 56, 111 and 132) would all benefit ered. The systematic errors obtained in this work are therefore only from further observations of all types, but are inherently more dif- lower limits on the potential systematics. Furthermore, stellar the- ficult to study as they are fainter and in more crowded fields than ory is notoriously unable to match the accurately-measured proper- the other TEPs. It therefore may be better to use the finite reser- ties for 0.7–1.1M¯ stars in eclipsing binary systems. The predicted voir of available telescope time on other systems which are equally radii are too small by up to 15%, and the Teffs are correspondingly deserving but also more straightforward to observe. too high. (Fig. 2). To illustrate this, I have also calculated the phys- On the methodological side, no changes are envisaged to the ical properties of the fourteen TEPs using, instead of stellar theory, photometric analyses presented in Paper I. The method in the cur- an empirical mass–radius relation obtained from well-studied low- rent work, however, could be improved in several ways. Firstly, an mass eclipsing binaries. This different approach can result in stellar increase in the number of stellar model sets used will allow more masses which are smaller by up to 15%, and all quantities (except robust systematic errors to be put forward. It may also be neces- the planet surface gravity) are affected to some extent. This proba- sary to investigate the effects of using different helium abundances bly sets an upper limit on the systematic errors present in measured (Claret 1995; Bertelli et al. 2008) or α-enhancement (Demarque properties of TEPs. Until we understand why models fail to match et al. 2004; Pietrinferni et al. 2006) in the stellar models. Secondly, the properties of eclipsing binary stars, we do not really know how the empirical mass–radius relation (Eq. 2) would be helped by the big the systematic uncertainties are in the measured properties of inclusion of new results (Ibanogluˇ et al. 2008; Clausen et al. 2008). the known TEPs. Thus our understanding of planets is limited by Finally, extension of the analysis to other well-observed TEPs will our understanding of low-mass stars. increase the statistical weight of the resulting sample of objects Temporarily putting aside the problems noted in the last para- with homogeneously determined properties. Slightly further into graph, the physical properties of the fourteen TEPs have been spec- the future, the expected deluge of new transiting extrasolar planets ified using the Claret stellar models, statistical uncertainties from from CoRoT and Kepler is eagerly awaited. the perturbation analysis, and systematic uncertainties from the interagreement between the Y2, Padova and Claret models (Tables 23 and 24). The agreement with literature results is mostly good, with the expection of the tricky system HD 149026. In particular, my results are in excellent agreement with the homogeneous study of TEPs published by TWH08, despite substantial methodological 7 ACKNOWLEDGEMENTS variations between the two studies. The resulting properties of the fourteen TEPs have been aug- I am indebted to Peter Wheatley for extensive discussions, and mented with literature results for all others for which a published to Tom Marsh, Boris Gansicke,¨ Antonio Claret and Josh Winn study is available. The mass–radius plot for the planets shows a for useful comments. I acknowledge the anonymous referee for a heavy clustering in the region 0.9–1.1MJup and 0.9–1.5RJup, with timely and robust report. I am grateful to John Eldridge and Anto- two outliers to lower masses (HD 149026 b and GJ 436 b) and a nio Claret for calculating large sets of stellar models for me. I ac- number of objects with higher masses but similar radii. Observa- knowledge financial support from STFC in the form of a postdoc- tional selection effects mean that these systems represent only the toral research assistant position. The following internet-based re- tip of the iceberg, so not many conclusions can be drawn from such sources were heavily used in research for this paper: the NASA As- a diagram at present. trophysics Data System; the SIMBAD database operated at CDS, The correlation between orbital period and planetary surface Strasbourg, France; and the arχiv scientific paper preprint service gravity (Southworth et al. 2007b) was revisited and found to be operated by Cornell University.

°c 0000 RAS, MNRAS 000, 000–000 22 John Southworth

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APPENDIX A: COMPARISON BETWEEN THE SYSTEM PROPERTIES DERIVED IN THIS WORK AND THOSE PRESENTED IN THE LITERATURE. This Appendix contains versions of the tables of physical properties of the TEPs in the main section, which have been extended to include comparisons with all previously published values of these properties.

°c 0000 RAS, MNRAS 000, 000–000 Homogeneous studies of transiting extrasolar planets. II. 25

Table A1. Derived physical properties of the TrES-1 system compared to literature determinations.

This work This work This work This work This work This work (mass–radius) (Padova models) (Siess models) (Y2 models) (Cambridge models) (Claret models)

a (AU) 0.0373 ± 0.0001 0.03954 ± 0.00036 0.04035 ∗ ± 0.00023 0.03946 ± 0.00034 0.03942 ± 0.00017 0.04000 ± 0.00043 ∗ MA (M¯) 0.752 ± 0.066 0.897 ± 0.025 0.954 ± 0.016 0.892 ± 0.023 0.890 ± 0.012 0.929 ± 0.030 ∗ RA (R¯) 0.772 ± 0.031 0.819 ± 0.015 0.836 ± 0.020 0.818 ± 0.015 0.817 ± 0.015 0.829 ± 0.015 ∗ loggA (cgs) 4.539 ± 0.017 4.564 ± 0.018 4.573 ± 0.014 4.563 ± 0.018 4.563 ± 0.016 4.569 ± 0.018 ∗ ρA (ρ¯) 1.632 ± 0.093 1.632 ± 0.092 1.632 ± 0.092 1.632 ± 0.092 1.632 ± 0.092 1.632 ± 0.092 ∗ Mb (MJup) 0.678 ± 0.054 0.763 ± 0.043 0.795 ± 0.044 0.760 ± 0.043 0.759 ± 0.041 0.781 ± 0.045 ∗ Rb (RJup) 1.038 ± 0.041 1.101 ± 0.031 1.124 ± 0.030 1.099 ± 0.030 1.098 ± 0.029 1.114 ± 0.032 −1 gb ( m s ) 15.6 ± 1.2 15.6 ± 1.2 15.6 ± 1.2 15.6 ± 1.2 15.6 ± 1.2 15.6 ± 1.2 ∗ ρb (ρJup) 0.606 ± 0.060 0.572 ± 0.055 0.560 ± 0.054 0.573 ± 0.055 0.573 ± 0.055 0.565 ± 0.054 +3.9 ∗ +0.0 +2.1 +1.8 +4.1 Age (Gyr) 1.0−1.6 0.1 −0.0 3.4−2.1 0.1−0.0 1.2−1.8 Alonso et al. (2004) Winn et al. (2007b) TWH08

+0.00056 Orbital semimajor axis a (AU) 0.0393 ± 0.0011 0.03925−0.00060 +0.038 Stellar mass MA (M¯) 0.88 ± 0.07 0.81 (ﬁxed) 0.878−0.040 +0.017 Stellar radius RA (R¯) 0.80 to 0.95 0.811 ± 0.020 0.807−0.016 +0.012 Stellar surface gravity loggA (cgs) 4.567−0.015 +0.001 Stellar density ρA (ρ¯) 1.704−0.085 +0.047 Planetary mass Mb (MJup) 0.75 ± 0.07 0.752−0.046 +0.18 +0.022 Planetary radius Rb (RJup) 1.08−0.04 1.081 ± 0.029 1.067−0.021 −1 +0.9 Planetary surface gravity gb ( m s ) 16.6−1.0 +0.056 Planetary density ρb (ρJup) 0.620−0.052

Table A2. Derived physical properties of the TrES-2 system compared to literature determinations.

This work This work This work This work This work This work (mass–radius) (Padova models) (Siess models) (Y2 models) (Cambridge models) (Claret models)

a (AU) 0.0352 ± 0.0010 0.03537 ± 0.00061 0.03666 ± 0.00063 0.03559 ± 0.00051 0.03708 ± 0.00024 0.03568 ± 0.00056

Mb (MJup) 1.180 ± 0.069 1.186 ± 0.045 1.274 ± 0.048 1.201 ± 0.039 1.303 ± 0.026 1.206 ± 0.042 Rb (RJup) 1.213 ± 0.048 1.216 ± 0.040 1.260 ± 0.041 1.224 ± 0.039 1.275 ± 0.037 1.226 ± 0.040 −1 gb ( m s ) 19.9 ± 1.2 19.9 ± 1.2 19.9 ± 1.2 19.9 ± 1.2 19.9 ± 1.2 19.9 ± 1.2 ρb (ρJup) 0.662 ± 0.060 0.660 ± 0.057 0.636 ± 0.055 0.655 ± 0.057 0.629 ± 0.054 0.654 ± 0.057 +1.9 +1.3 +1.2 +1.6 Age (Gyr) 4.5 ± 2.1 1.5−2.0 4.5−1.7 0.1−0.1 5.3−2.6 O’Donovan et al. (2006) Sozzetti et al. (2007) Holman et al. (2007b) TWH08

+0.0012 +0.00070 a (AU) 0.0367−0.0005 0.03558−0.00077 +0.11 +0.059 MA (M¯) 1.08−0.05 0.980 ± 0.062 0.983−0.063 +0.06 +0.036 +0.033 RA (R¯) 1.00−0.04 1.000−0.033 1.003 ± 0.027 1.003−0.033 +0.021 +0.019 loggA (cgs) 4.429−0.023 4.427−0.021 +0.043 ρA (ρ¯) 09.76 ± 0.046 0.974−0.042 +0.09 +0.051 Mb (MJup) 1.28−0.04 1.198 ± 0.053 1.200−0.053 +0.09 +0.041 Rb (RJup) 1.24−0.06 1.222 ± 0.038 1.224−0.041 −1 +0.75 gb ( m s ) 19.76 ± 0.91 19.9−0.72 +0.10 +0.0.77 ρb (ρJup) 0.67−0.07 0.655−0.067

°c 0000 RAS, MNRAS 000, 000–000 26 John Southworth

Table A3. Derived physical properties of the XO-1 system compared to literature determinations.

This work This work This work This work This work This work (mass–radius) (Padova models) (Siess models) (Y2 models) (Cambridge models) (Claret models)

a (AU) 0.0465 ± 0.0013 0.04909 ± 0.00026 0.05002∗ ± 0.00035 0.04929 ± 0.00023 0.04909 ± 0.00031 0.04990 ± 0.00029 ∗ MA (M¯) 0.863 ± 0.072 1.015 ± 0.016 1.074 ± 0.023 1.028 ± 0.015 1.015 ± 0.019 1.066 ± 0.018 ∗ RA (R¯) 0.886 ± 0.037 0.935 ± 0.025 0.953 ± 0.027 0.939 ± 0.024 0.935 ± 0.025 0.950 ± 0.022 ∗ loggA (cgs) 4.480 ± 0.018 4.503 ± 0.016 4.511 ± 0.016 4.505 ± 0.017 4.503 ± 0.016 4.510 ± 0.018 ∗ ρA (ρ¯) 1.242 ± 0.078 1.242 ± 0.080 1.242 ± 0.080 1.242 ± 0.080 1.242 ± 0.080 1.242 ± 0.080 ∗ Mb (MJup) 0.818 ± 0.078 0.911 ± 0.071 0.946 ± 0.075 0.918 ± 0.072 0.911 ± 0.072 0.941 ± 0.074 ∗ Rb (RJup) 1.135 ± 0.046 1.198 ± 0.037 1.220 ± 0.038 1.203 ± 0.037 1.198 ± 0.037 1.218 ± 0.038 −1 gb ( m s ) 15.8 ± 1.5 15.8 ± 1.5 15.8 ± 1.5 15.8 ± 1.5 15.8 ± 1.547 15.8 ± 1.5 ∗ ρb (ρJup) 0.559 ± 0.068 0.530 ± 0.063 0.520 ± 0.062 0.528 ± 0.063 0.530 ± 0.063 0.521 ± 0.062 +0.1 ∗ +0.2 +0.7 +0.2 +1.3 Age (Gyr) 0.6−0.0 0.1 −0.0 1.4−1.3 0.3−0.1 0.1−0.0 McCullough et al. (2006) Wilson et al. (2006) Holman et al. (2006) TWH08

+0.00089 a (AU) 0.0488 ± 0.0005 0.04928−0.00099 +0.057 MA (M¯) 1.0 ± 0.03 1.00 ± 0.03 ﬁxed 1.027−0.061 +0.018 +0.037 RA (R¯) 1.0 ± 0.08 1.0 ± 0.08 0.928−0.013 0.934−0.032 +0.018 loggA (cgs) 4.53 ± 0.065 4.509−0.027 +0.010 ρA (ρ¯) 1.333−0.149 +0.081 Mb (MJup) 0.90 ± 0.07 0.9 ﬁxed 0.918−0.078 +0.028 +0.047 Rb (RJup) 1.30 ± 0.11 1.34 ± 0.12 1.184−0.018 1.206−0.042 −1 +1.4 gb ( m s ) 16.3−1.5 +0.077 ρb (ρJup) 0.41 ± 0.10 0.54 ± 0.06 0.524−0.069

Table A4. Derived physical properties of the WASP-1 system compared to literature determinations.

This work This work This work This work This work (mass–radius) (Siess models) (Y2 models) (Cambridge models) (Claret models)

+0.0011 +0.00040 +0.00037 +0.00035 +0.00031 a (AU) 0.0417−0.0014 0.03955−0.00044 0.03944−0.00044 0.03815−0.00047 0.03933−0.00032 +0.11 +0.040 +0.037 +0.033 +0.031 MA (M¯) 1.52−0.12 1.299−0.043 1.288−0.043 1.166−0.043 1.278−0.031 +0.08 +0.060 +0.056 +0.054 +0.055 RA (R¯) 1.56−0.12 1.477−0.082 1.473−0.086 1.424−0.083 1.469−0.083 +0.035 +0.044 +0.043 +0.043 +0.044 loggA (cgs) 4.236−0.023 4.213−0.026 4.212−0.027 4.197−0.027 4.211−0.026 +0.069 +0.069 +0.069 +0.069 +0.069 ρA (ρ¯) 0.403−0.037 0.403−0.037 0.403−0.037 0.403−0.037 0.403−0.037 +0.11 +0.090 +0.089 +0.083 +0.088 Mb (MJup) 1.02−0.12 0.917−0.090 0.912−0.090 0.853−0.084 0.907−0.088 +0.07 +0.060 +0.060 +0.057 +0.059 Rb (RJup) 1.59−0.11 1.506−0.093 1.502−0.092 1.453−0.089 1.498−0.091 −1 +1.6 +1.6 +1.6 +1.6 +1.6 gb ( m s ) 10.0−1.2 10.0−1.2 10.0−1.2 10.0−1.2 10.0−1.2 +0.058 +0.061 +0.061 +0.063 +0.061 ρb (ρJup) 0.255−0.037 0.268−0.039 0.269−0.039 0.278−0.040 0.270−0.039 +0.4 +0.4 Age (Gyr) 2.7−0.6 2.8 ± 0.5 2.9 ± 0.4 3.1−0.5 Collier Cameron Shporer et al. (2007) Charbonneau Stempels et al. (2007) TWH08 et al. (2007) et al. (2007)

+0.00049 a (AU) 0.0369 to 0.0395 0.03946−0.00048 +0.68 +0.049 MA (M¯) 1.24−0.20 1.15 ﬁxed 1.453 ± 0.032 1.25 to 1.35 1.301−0.047 +0.24 +0.052 RA (R¯) 1.15−0.09 1.415 ± 0.074 1.45 ± 0.08 1.517−0.045 +0.020 loggA (cgs) 4.28 ± 0.15 4.190−0.022 +0.006 ρA (ρ¯) 0.390−0.042 +0.091 Mb (MJup) 0.80 to 0.98 0.867 ± 0.073 0.918−0.090 +0.052 Rb (RJup) 1.33 to 2.53 1.398 ± 0.076 1.443 ± 0.039 1.514−0.047 −1 +1.1 gb ( m s ) 10.2−1.1 +0.039 ρb (ρJup) 0.264−0.035

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Table A5. Derived physical properties of the WASP-2 system compared to literature determinations.

This work This work This work This work This work This work (mass–radius) (Padova models) (Siess models) (Y2 models) (Cambridge models) (Claret models)

a (AU) 0.0301 ± 0.0011 0.0309 ± 0.0013 0.0321 ± 0.0010 0.0310 ± 0.0011 0.0312 ± 0.0009 0.0312 ± 0.0013

Mb (MJup) 0.841 ± 0.085 0.885 ± 0.100 0.956 ± 0.094 0.893 ± 0.089 0.906 ± 0.084 0.905 ± 0.099 Rb (RJup) 1.030 ± 0.069 1.056 ± 0.076 1.098 ± 0.073 1.061 ± 0.071 1.069 ± 0.069 1.068 ± 0.075 −1 gb ( m s ) 19.7 ± 2.7 19.7 ± 2.7 19.7 ± 2.7 19.7 ± 2.7 19.7 ± 2.7 19.7 ± 2.7 ρb (ρJup) 0.77 ± 0.15 0.75 ± 0.14 0.72 ± 0.14 0.75 ± 0.14 0.74 ± 0.14 0.74 ± 0.14

Collier Cameron et al. (2007) Charbonneau et al. (2007) TWH08

+0.00130 a (AU) 0.0296 to 0.0318 0.03138−0.00154 +0.15 +0.12 MA (M¯) 0.79−0.04 0.813 ± 0.032 0.89−0.12 +0.062 RA (R¯) 0.78 ± 0.06 0.81 ± 0.04 0.840−0.065 +0.035 loggA (cgs) 4.537−0.046 +0.19 ρA (ρ¯) 1.45−0.11 +0.090 Mb (MJup) 0.81 to 0.95 0.915−0.093 +0.080 Rb (RJup) 0.65 to 1.26 1.038 ± 0.050 1.071−0.083 −1 +1.8 gb ( m s ) 19.4−1.4 +0.22 ρb (ρJup) 0.74−0.16

Table A6. Derived physical properties of the HAT-P-1 system compared to literature determinations.

This work This work This work This work This work This work (mass–radius) (Padova models) (Siess models) (Y2 models) (Cambridge models) (Claret models)

a (AU) 0.05401 ± 0.00149 0.05540 ± 0.00038 0.05669 ± 0.00033 0.05529 ± 0.00043 0.05464 ± 0.00050 0.05570 ± 0.00049

Mb (MJup) 0.507 ± 0.033 0.533 ± 0.020 0.558 ± 0.021 0.531 ± 0.020 0.519 ± 0.020 0.539 ± 0.021 Rb (RJup) 1.179 ± 0.049 1.209 ± 0.039 1.237 ± 0.040 1.207 ± 0.039 1.192 ± 0.039 1.216 ± 0.040 −1 gb ( m s ) 9.05 ± 0.66 9.05 ± 0.66 9.05 ± 0.66 9.05 ± 0.66 9.05 ± 0.66 9.05 ± 0.66 ρb (ρJup) 0.309 ± 0.033 0.302 ± 0.031 0.295 ± 0.030 0.302 ± 0.031 0.306 ± 0.031 0.300 ± 0.031 +1.4 +0.4 +0.8 +1.5 +1.1 Age (Gyr) 0.7−1.0 0.1−0.0 2.1−1.0 1.1−1.1 1.6−1.3 Bakos et al. (2007a) Winn et al. (2007c) TWH08 Johnson et al. (2008)

+0.0012 a (AU) 0.0551 ± 0.0015 0.0551 ± 0.0015 0.0553−0.0013 +0.075 MA (M¯) 1.12 ± 0.09 fixed 1.12 ± 0.09 fixed 1.133−0.079 1.133 ± 0.077 fixed +0.10 +0.048 RA (R¯) 1.15−0.07 fixed 1.115 ± 0.043 1.135−0.048 1.115 ± 0.050 +0.027 loggA (cgs) 4.382−0.030 +0.053 ρA (ρ¯) 0.809 ± 0.071 0.775−0.050 +0.030 Mb (MJup) 0.53 ± 0.04 0.53 ± 0.04 fixed 0.532−0.03 0.524 ± 0.031 +0.11 +0.053 Rb (RJup) 1.36−0.09 1.203 ± 0.051 1.242−0.053 1.225 ± 0.059 −1 +0.51 gb ( m s ) 9.045 ± 0.0661 8.53−0.48 +0.043 ρb (ρJup) 0.303 ± 0.025 0.278−0.024

°c 0000 RAS, MNRAS 000, 000–000 28 John Southworth

Table A7. Derived physical properties of the OGLE-TR-10 system compared to literature determinations.

This work This work This work This work This work (mass–radius) (Siess models) (Y2 models) (Cambridge models) (Claret 2008)

a (AU) 0.04492 ± 0.0017 0.04464 ± 0.00051 0.04476 ± 0.00064 0.04278 ± 0.00071 0.04471 ± 0.00059

Mb (MJup) 0.67 ± 0.15 0.66 ± 0.14 0.67 ± 0.14 0.61 ± 0.13 0.66 ± 0.14 Rb (RJup) 1.28 ± 0.11 1.27 ± 0.10 1.27 ± 0.10 1.22 ± 0.10 1.27 ± 0.10 −1 gb ( m s ) 10.2 ± 2.7 10.2 ± 2.7 10.2 ± 2.7 10.2 ± 2.7 10.1 ± 2.7 ρb (ρJup) 0.32 ± 0.11 0.32 ± 0.11 0.32 ± 0.11 0.34 ± 0.11 0.32 ± 0.11 +1.2 +1.2 +1.5 Age (Gyr) 2.0−1.5 2.0 ± 1.1 2.6−1.1 2.0−1.4 Bouchy et al. (2005a) Konacki et al. (2005) Pont et al. (2007) Holman et al. (2007a) TWH08

+0.0013 a (AU) 0.04162 ± 0.00069 0.0434−0.0015 +0.13 +0.10 MA (M¯) 1.22 ± 0.045 1.00 ± 0.05 fixed 1.18 ± 0.04 1.03−0.12 1.14−0.12 +0.19 +0.13 RA (R¯) 1.21 ± 0.066 1.00 ± 0.10 fixed 1.16 ± 0.06 1.06−0.16 1.17−0.11 +0.064 loggA (cgs) 4.358−0.082 +0.13 ρA (ρ¯) 0.73−0.17 +0.14 Mb (MJup) 0.66 ± 0.21 0.57 ± 0.12 0.63 ± 0.14 0.57 ± 0.12 fixed 0.62−0.14 +0.14 Rb (RJup) 1.54 ± 0.12 1.24 ± 0.09 1.26 ± 0.07 1.06 ± 0.08 1.25−0.12 −1 +2.9 gb ( m s ) 10.0−2.6 +0.15 +0.15 ρb (ρJup) 0.31 ± 0.08 0.34−0.11 0.32−0.10

Table A8. Derived physical properties of the OGLE-TR-56 system compared to literature determinations.

This work This work This work This work This work (mass–radius) (Siess models) (Y2 models) (Cambridge models) (Claret models)

a (AU) 0.02381 ± 0.00137 0.02407 ± 0.00030 0.02390 ± 0.00034 0.02303 ± 0.00031 0.02395 ± 0.00029

Mb (MJup) 1.29 ± 0.18 1.32 ± 0.14 1.30 ± 0.14 1.21 ± 0.13 1.31 ± 0.14 Rb (RJup) 1.20 ± 0.18 1.21 ± 0.17 1.21 ± 0.17 1.16 ± 0.17 1.21 ± 0.17 −1 gb ( m s ) 22.3 ± 7.0 22.3 ± 7.0 22.3 ± 7.0 22.3 ± 7.0 22.3 ± 7.0 ρb (ρJup) 0.75 ± 0.35 0.74 ± 0.34 0.74 ± 0.35 0.77 ± 0.36 0.74 ± 0.35 +1.4 +0.9 +0.8 +1.3 Age (Gyr) 1.2−1.2 1.8−1.4 2.0−2.0 1.6−1.5 Konacki et al. Torres et al. Bouchy et al. Santos et al. Pont et al. TWH08 (2003a) (2004) (2005a) (2006) (2007)

+0.00046 a (AU) 0.0225 0.0225 ± 0.0004 0.02383−0.00051 +0.072 MA (M¯) 1.04 ± 0.05 1.04 ± 0.05 ﬁxed 1.10 ± 0.078 1.17 ± 0.04 1.17 ± 0.04 1.228−0.078 +0.089 RA (R¯) 1.10 ± 0.10 1.10 ± 0.10 ﬁxed 1.12 ± 0.069 1.15 ± 0.06 1.32 ± 0.06 1.363−0.086 +0.043 loggA (cgs) 4.258−0.043 +0.078 ρA (ρ¯) 0.479−0.055 +0.18 Mb (MJup) 0.9 ± 0.3 1.45 ± 0.23 1.18 ± 0.13 1.24 ± 0.13 1.29 ± 0.12 1.39−0.17 +0.092 Rb (RJup) 1.30 ± 0.15 1.23 ± 0.16 1.25 ± 0.09 1.25 ± 0.08 1.30 ± 0.05 1.363−0.090 −1 +3.0 gb ( m s ) 18.4−2.7 +0.27 +0.15 ρb (ρJup) 0.7 ± 0.4 1.4 ± 0.4 0.59−0.20 0.55−0.11

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Table A9. Derived physical properties of the OGLE-TR-111 system compared to literature determinations.

This work This work This work This work This work This work (mass–radius) (Padova models) (Siess models) (Y2 models) (Cambridge models) (Claret models)

a (AU) 0.04616 ± 0.00162 0.04650 ± 0.00112 0.04745 ± 0.00088 0.04676 ± 0.00067 0.04511 ± 0.00077 0.04702 ± 0.00073

Mb (MJup) 0.532 ± 0.103 0.540 ± 0.100 0.562 ± 0.103 0.546 ± 0.099 0.508 ± 0.093 0.552 ± 0.101 Rb (RJup) 1.069 ± 0.075 1.077 ± 0.070 1.099 ± 0.070 1.083 ± 0.067 1.045 ± 0.066 1.089 ± 0.068 −1 gb ( m s ) 11.5 ± 2.5 11.5 ± 2.5 11.5 ± 2.5 11.5 ± 2.5 11.5 ± 2.5 11.5 ± 2.5 ρb (ρJup) 0.44 ± 0.11 0.44 ± 0.11 0.52 ± 0.14 0.43 ± 0.11 0.45 ± 0.11 0.43 ± 0.11 +9.9 +3.4 +4.2 +2.0 +5.4 Age (Gyr) 10.8−7.9 10.0−8.8 9.9−4.4 14.3−6.2 11.5−7.0 Pont et al. Gallardo et Santos et al. Silva & Cruz Winn et al. Minniti et al. TWH08 Diaz et al. (2004) al. (2005) (2006) (2006) (2007a) (2007) (2008)

+0.050 +0.0010 a (AU) 0.047 ± 0.001 0.047 ± 0.001 0.0467−0.065 0.04689−0.00097 +0.15 +0.058 MA (M¯) 0.82−0.02 0.81 ± 0.02 0.96 ± 0.21 0.81 ± 0.02 fixed 0.82 ± 0.02 fixed 0.852−0.052 0.81 fixed +0.10 +0.045 +0.041 RA (R¯) 0.85−0.03 0.71 ± 0.02 0.83 ± 0.02 0.831 ± 0.031 0.83 ± 0.03 fixed 0.831−0.040 0.81−0.048 +0.038 loggA (cgs) 4.529−0.042 +0.17 ρA (ρ¯) 1.47−0.16 +0.10 Mb (MJup) 0.53 ± 0.11 0.52 ± 0.13 0.52 fixed 0.53 fixed 0.55−0.10 0.52 fixed +0.13 +0.065 +0.057 +0.057 Rb (RJup) 1.00−0.06 0.94 ± 0.03 0.97 ± 0.06 1.16 ± 0.19 1.067 ± 0.054 1.006−0.048 1.051−0.052 0.922−0.062 −1 +2.5 gb ( m s ) 12.2−2.4 +0.31 +0.13 ρb (ρJup) 0.49−0.21 0.6 ± 0.2 0.48−0.11

Table A10. Derived physical properties of the OGLE-TR-132 system compared to literature determinations.

This work (mass–radius) This work (Y2 models) This work (Cambridge models) This work (Claret models)

a (AU) 0.03081 ± 0.00160 0.03050 ± 0.00034 0.02879 ± 0.00044 0.03040 ± 0.00033

MA (M¯) 1.365 ± 0.213 1.325 ± 0.044 1.114 ± 0.051 1.311 ± 0.043 RA (R¯) 1.397 ± 0.201 1.38 ± 0.14 1.31 ± 0.14 1.38 ± 0.14 loggA (cgs) 4.283 ± 0.062 4.278 ± 0.079 4.253 ± 0.079 4.277 ± 0.079 ρA (ρ¯) 0.50 ± 0.15 0.50 ± 0.15 0.50 ± 0.15 0.50 ± 0.15

Mb (MJup) 1.02 ± 0.32 1.00 ± 0.30 0.89 ± 0.27 1.00 ± 0.30 Rb (RJup) 1.28 ± 0.17 1.26 ± 0.15 1.19 ± 0.15 1.26 ± 0.15 −1 gb ( m s ) 15.6 ± 6.1 15.6 ± 6.1 15.6 ± 6.1 15.6 ± 6.1 ρb (ρJup) 0.49 ± 0.24 0.50 ± 0.24 0.53 ± 0.26 0.50 ± 0.24 +0.6 +0.5 +0.6 Age (Gyr) 1.4−1.1 1.9−1.3 1.5−1.4 Bouchy et al. (2004) Moutou et al. (2004) Gillon et al. (2007c) TWH08

+0.00057 a (AU) 0.0306 ± 0.0008 0.03035−0.00053 +0.075 MA (M¯) 1.34 ± 0.10 1.35 ± 0.06 1.26 ± 0.03 1.305−0.067 +0.49 +0.17 RA (R¯) 1.41−0.10 1.43 ± 0.10 1.34 ± 0.08 1.32−0.12 +0.063 loggA (cgs) 4.313−0.090 +0.21 ρA (ρ¯) 0.51−0.09 +0.14 Mb (MJup) 1.01 ± 0.31 1.19 ± 0.13 1.14 ± 0.12 1.18−0.13 +0.80 +0.15 Rb (RJup) 1.15−0.13 1.13 ± 0.08 1.18 ± 0.07 1.20−0.11 −1 +4.9 gb ( m s ) 18.9−3.3 +0.3 +0.22 +0.26 ρb (ρJup) 0.6−0.5 0.82 ± 0.27 0.69−0.17 0.69−0.21

°c 0000 RAS, MNRAS 000, 000–000 30 John Southworth

Table A11. Derived physical properties of the GJ 436 system compared to literature determinations.

This work This work This work This work This work (mass–radius) (Padova models) (Siess models) (Y2 models) (Claret models)

a (AU) 0.0282 ± 0.0013 0.02928 ± 0.00070 0.02995 ± 0.00042 0.02882 ± 0.00066 0.02972 ± 0.0010

Mb (MJup) 0.0704 ± 0.0069 0.0757 ± 0.0042 0.0793 ± 0.0032 0.0734 ± 0.0039 0.0781 ± 0.0059 Rb (RJup) 0.357 ± 0.022 0.371 ± 0.017 0.379 ± 0.015 0.365 ± 0.016 0.376 ± 0.019 −1 gb ( m s ) 13.7 ± 1.1 13.7 ± 1.1 13.7 ± 1.1 13.7 ± 1.1 13.7 ± 1.1 ρb (ρJup) 1.54 ± 0.20 1.49 ± 0.18 1.45 ± 0.17 1.51 ± 0.18 1.47 ± 0.18

Gillon et al. (2007a) Gillon et al. (2007b) Deming et al. Torres (2007) TWH08 Alonso et al. Shporer et al. Bean et al. (2008) (2007) (2008) (2008a)

+0.00029 +0.00030 a (AU) 0.0291 ± 0.0004 0.02872 ± 0.00027 0.02872−0.00026 0.02872 0.02872−0.00025 +0.014 +0.014 +0.014 MA (M¯) 0.44 ± 0.04 fixed 0.44 ± 0.04 fixed 0.47 ± 0.02 0.452−0.012 0.452−0.012 0.452−0.012 fixed 0.44 ± 0.04 fixed +0.22 +0.009 +0.009 +0.029 RA (R¯) 0.44 ± 0.04 fixed 0.463−0.17 0.47 ± 0.02 0.464−0.011 0.464−0.011 0.45 ± 0.02 0.505−0.020 +0.018 loggA (cgs) 4.843−0.011 +0.618 ρA (ρ¯) 4.565−0.568 +0.0025 Mb (MJup) 0.0711 ± 0.006 0.0711 ± 0.006 0.070 ± 0.003 0.0729 ± 0.0025 0.0729−0.0025 0.0729 0.073 ± 0.003 0.0717 ± 0.047 +0.037 +0.019 +0.008 +0.0082 +0.040 Rb (RJup) 0.352−0.025 0.374−0.014 0.386 ± 0.016 0.376−0.009 0.3767−0.0092 0.37 ± 0.01 0.437−0.029 −1 +1.2 gb ( m s ) 12.8 ± 1.2 12.8−1.2 +0.11 +0.11 +0.13 ρb (ρJup) 1.4 1.36−0.10 1.36−0.10 0.72−0.19

Table A12. Derived physical properties of the HD 149026 system compared to literature determinations.

This work (mass–radius) This work (Y2 models) This work (Cambridge models) This work (Claret models)

+0.0020 +0.00034 +0.0050 +0.00037 a (AU) 0.0427−0.0013 0.04303−0.00026 0.04060−0.0032 0.04294−0.00021 +0.19 +0.031 +0.040 +0.033 MA (M¯) 1.26−0.11 1.285−0.023 1.079−0.026 1.277−0.019 +0.17 +0.121 +0.116 +0.12 RA (R¯) 1.28−0.09 1.295−0.058 1.221−0.057 1.292−0.054 +0.030 +0.037 +0.037 +0.039 loggA (cgs) 4.319−0.054 4.322−0.068 4.297−0.068 4.321−0.069 +0.083 +0.083 +0.083 +0.083 ρA (ρ¯) 0.592−0.129 0.592−0.129 0.592−0.129 0.592−0.129 +0.035 +0.011 +0.012 +0.012 Mb (MJup) 0.353−0.024 0.358−0.011 0.319−0.010 0.357−0.011 +0.110 +0.099 +0.094 +0.099 Rb (RJup) 0.608−0.047 0.612−0.072 0.578−0.068 0.611−0.072 −1 +6.8 +6.8 +6.8 +6.8 gb ( m s ) 23.7−6.2 23.7−6.2 23.7−6.2 23.7−6.2 +0.71 +0.71 +0.76 +0.71 ρb (ρJup) 1.57−0.58 1.56−0.57 1.65−0.60 1.56−0.57 +0.8 +0.7 Age (Gyr) 1.2−0.6 1.2 ± 1.0 1.9−0.4 Sato et al. (2005) Charbonneau Masana et al. Wolf et al. (2007) Winn et al. (2008a) TWH08 Nutzman et al. et al. (2006) (2006) (2008)

+0.0028 a (AU) 0.042 0.04313−0.0037 +0.060 MA (M¯) 1.3 ± 0.1 1.30 ± 0.10 fixed 1.30 ± 0.10 fixed 1.30 ± 0.06 fixed 1.294−0.050 1.30 ± 0.10 fixed +0.120 RA (R¯) 1.45 ± 0.1 1.45 ± 0.10 fixed 1.515 ± 0.096 1.45 ± 0.10 fixed 1.45 ± 0.10 fixed 1.368−0.083 1.497 ± 0.069 +0.045 loggA (cgs) 4.278−0.063 +0.008 ρA (ρ¯) 0.584−0.177 +0.022 Mb (MJup) 0.36 ± 0.04 0.352 ± 0.025 0.36 ± 0.03 0.359−0.021 0.359 ± 0.006 +0.060 Rb (RJup) 0.725 ± 0.05 0.726 ± 0.064 0.718 ± 0.065 0.71 ± 0.05 0.654−0.045 0.755 ± 0.040 −1 +0.4 +2.4 +1.9 gb ( m s ) 22.8−5.9 22.9−4.2 16.0−1.7 +0.34 +0.31 ρb (ρJup) 0.86−0.024 1.28−0.29

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Table A13. Derived physical properties of the HD 189733 system compared to literature determinations.

This work This work This work This work This work This work (mass–radius) (Padova models) (Siess models) (Y2 models) (Cambridge models) (Claret models)

a (AU) 0.02932 ± 0.00097 0.03129 ± 0.00019 0.03189∗ ± 0.00024 0.03122 ± 0.00036 0.03144∗ ± 0.00021 0.03175 ± 0.00019 ∗ ∗ MA (M¯) 0.682 ± 0.067 0.830 ± 0.016 0.878 ± 0.020 0.824 ± 0.029 0.841 ± 0.017 0.866 ± 0.015 ∗ ∗ RA (R¯) 0.701 ± 0.036 0.749 ± 0.024 0.763 ± 0.027 0.747 ± 0.022 0.752 ± 0.025 0.760 ± 0.022 ∗ ∗ loggA (cgs) 4.580 ± 0.022 4.608 ± 0.023 4.616 ± 0.021 4.607 ± 0.025 4.610 ± 0.022 4.615 ± 0.024 ∗ ∗ ρA (ρ¯) 1.98 ± 0.16 1.98 ± 0.16 1.98 ± 0.16 1.98 ± 0.17 1.98 ± 0.17 1.98 ± 0.17 ∗ ∗ Mb (MJup) 1.023 ± 0.074 1.165 ± 0.037 1.210 ± 0.040 1.159 ± 0.043 1.176 ± 0.034 1.199 ± 0.038 ∗ ∗ Rb (RJup) 1.074 ± 0.047 1.146 ± 0.034 1.168 ± 0.035 1.143 ± 0.035 1.151 ± 0.034 1.163 ± 0.034 −1 gb ( m s ) 22.0 ± 1.4 22.0 ± 1.4 22.0 ± 1.4 22.0 ± 1.4 22.0 ± 1.4 22.0 ± 1.4 ∗ ∗ ρb (ρJup) 0.827 ± 0.080 0.774 ± 0.071 0.760 ± 0.069 0.776 ± 0.071 0.771 ± 0.070 0.763 ± 0.069 +2.9 ∗ +0.0 +4.2 ∗ +0.0 +3.3 Age (Gyr) 0.1−0.0 0.1 −0.0 3.7−4.1 0.1 −0.0 0.1−0.0 Bouchy et al. Bakos et al. Masana et al. Winn et al. Winn et al. Baines et al. TWH08 Miller-Ricci (2005b) (2006) (2006) (2006) (2007b) (2007) et al. (2008)

+0.00060 a (AU) 0.0313 ± 0.0004 0.03099−0.00063 +0.0048 MA (M¯) 0.83 ± 0.03 fixed 0.83 ± 0.03 fixed 0.82 ± 0.03 0.806−0.0048 0.82 ± 0.03 fixed +0.018 RA (R¯) 0.71 ± 0.02 fixed 0.758 ± 0.016 fixed 0.758 ± 0.016 0.73 ± 0.02 0.753 ± 0.025 0.779 ± 0.052 0.756−0.018 0.749 ± 0.009 +0.014 loggA (cgs) 4.587−0.015 +0.038 ρA (ρ¯) 1.867−0.038 +0.057 Mb (MJup) 1.15 ± 0.04 1.13 ± 0.03 1.144−0.056 +0.037 Rb (RJup) 1.26 ± 0.03 1.154 ± 0.033 1.10 ± 0.03 1.156 ± 0.046 1.19 ± 0.08 1.138−0.037 1.192 ± 0.019 −1 +0.72 gb ( m s ) 21 ± 2 21.9−0.69 +0.071 ρb (ρJup) 0.60 ± 0.06 ∼ 0.8 0.73 ± 0.15 0.776−0.064

∗ These results are for the youngest ages available so cannot be regarded as robustly determined (see text for discussion). This is particularly important for the quoted uncertainties which will be rendered artiﬁcally low by this circumstance.

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Table A14. Derived physical properties of the HD 209458 system compared to literature determinations.

This work This work This work This work This work This work (mass–radius) (Padova models) (Siess models) (Y2 models) (Cambridge models) (Claret models)

a (AU) 0.04724 ± 0.00105 0.04742 ± 0.00045 0.04888 ± 0.00032 0.04757 ± 0.00034 0.04799 ± 0.00029 0.04770 ± 0.00041

Mb (MJup) 0.693 ± 0.032 0.698 ± 0.016 0.742 ± 0.013 0.703 ± 0.013 0.715 ± 0.012 0.707 ± 0.015 Rb (RJup) 1.376 ± 0.032 1.381 ± 0.016 1.424 ± 0.014 1.386 ± 0.014 1.398 ± 0.013 1.389 ± 0.015 −1 gb ( m s ) 9.08 ± 0.17 9.08 ± 0.17 9.08 ± 0.17 9.08 ± 0.17 9.08 ± 0.17 9.08 ± 0.17 ρb (ρJup) 0.266 ± 0.009 0.265 ± 0.007 0.257 ± 0.007 0.264 ± 0.007 0.262 ± 0.007 0.263 ± 0.007 +0.9 +0.6 +0.6 +0.7 Age (Gyr) 1.7−0.7 0.2−0.1 2.3 ± 0.5 0.5−0.3 2.3−0.6 Charbonneau Henry et al. Mazeh et al. Queloz et al. Brown et al. Cody & Sasselov Mandel & Agol et al. (2000) (2000) (2000) (2000) (2001) (2002) (2002)

a (AU) 0.048 ± 0.001

MA (M¯) 1.1 fixed 1.03 fixed 1.1 ± 0.1 1.1 ± 0.1 fixed 1.06 ± 0.13 1.1 ± 0.1 fixed RA (R¯) 1.1 fixed 1.15 fixed 1.2 ± 0.1 1.2 ± 0.1 1.146 ± 0.050 1.18 ± 0.10 1.145 ± 0.035 loggA (cgs) ρA (ρ¯)

Mb (MJup) 0.63 0.69 ± 0.05 0.685 ± 0.02 +0.10 Rb (RJup) 1.27 ± 0.02 1.42 ± 0.10 1.40 ± 0.18 1.4 ± 0.17 1.347 ± 0.060 1.42−0.13 1.376 ± 0.043 −1 gb ( m s ) 9.7 9.43 ρb (ρJup) 0.31 0.22 ± 0.03 0.25 ± 0.06 0.28 0.24

Winn et al. Wittenmyer et al. Richardson et al. Masana et al. Knutson et al. TWH08 Miller-Ricci Kipping (2005) (2005) (2006) (2006) (2007) et al. (2008) (2008)

+0.00046 a (AU) 0.04707−0.00047 +0.033 +0.096 MA (M¯) 1.06 ﬁxed 1.093 ± 0.092 1.171 1.101 ± 0.066 1.119−0.033 1.101 ± 0.064 1.163−0.079 +0.014 +0.055 RA (R¯) 1.15 ± 0.05 1.145 ± 0.056 1.064 ± 0.069 1.164 ± 0.057 1.125 ± 0.023 1.155−0.016 1.118 ± 0.03 1.072−0.052 +0.007 loggA (cgs) 4.361−0.008 +0.010 ρA (ρ¯) 0.727−0.010 0.94 ± 0.16 +0.015 Mb (MJup) 0.657 ± 0.064 0.657 ± 0.052 0.64 ± 0.06 0.685−0.014 0.681 ± 0.039 +0.016 Rb (RJup) 1.35 ± 0.06 1.350 ± 0.066 1.265 ± 0.085 1.320 ± 0.025 1.359−0.019 1.339 ± 0.04 1.275 ± 0.082 −1 +0.11 gb ( m s ) 9.18−0.11 +0.013 ρb (ρJup) 0.278 ± 0.040 0.272−0.011 0.264 ± 0.052

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Table A15. The physical properties of the stellar components of the TEPs studied in this work, derived using the empirical mass–radius relation.

System Mass (M¯) Radius (R¯) logg [cm/s] Density (ρ¯) TrES-1 0.752 ± 0.066 0.772 ± 0.031 4.539 ± 0.017 1.632 ± 0.093 TrES-2 0.958 ± 0.081 0.983 ± 0.049 4.435 ± 0.022 1.008 ± 0.092 XO-1 0.863 ± 0.072 0.886 ± 0.037 4.480 ± 0.018 1.242 ± 0.078 +0.11 +0.08 +0.035 +0.069 WASP-1 1.52−0.12 1.56−0.12 4.236−0.023 0.403−0.037 WASP-2 0.784 ± 0.085 0.805 ± 0.061 4.520 ± 0.032 1.50 ± 0.21 HAT-P-1 1.054 ± 0.087 1.080 ± 0.055 4.394 ± 0.022 0.837 ± 0.076 OGLE-TR-10 1.26 ± 0.14 1.29 ± 0.12 4.319 ± 0.041 0.59 ± 0.11 OGLE-TR-56 1.23 ± 0.21 1.29 ± 0.20 4.330 ± 0.070 0.62 ± 0.21 OGLE-TR-111 0.814 ± 0.085 0.835 ± 0.061 4.505 ± 0.031 1.40 ± 0.19 OGLE-TR-132 1.37 ± 0.21 1.40 ± 0.20 4.283 ± 0.062 0.50 ± 0.15 GJ 436 0.429 ± 0.060 0.443 ± 0.031 4.777 ± 0.031 4.92 ± 0.55 +0.19 +0.17 +0.030 +0.083 HD 149026 1.26−0.11 1.28−0.09 4.319−0.054 0.592−0.129 HD 189733 0.682 ± 0.067 0.701 ± 0.036 4.580 ± 0.022 1.98 ± 0.16 HD 209458 1.132 ± 0.076 1.159 ± 0.026 4.364 ± 0.010 0.727 ± 0.005

Table A16. The physical properties of the planetary components of the TEPs studied in this work, derived using the empirical mass–radius relation.

−1 System Semimajor axis (AU) Mass (MJup) Radius (RJup) Gravity ( m s ) Density (ρJup) TrES-1 b 0.0373 ± 0.0011 0.678 ± 0.054 1.038 ± 0.041 15.6 ± 1.2 0.606 ± 0.060 TrES-2 b 0.0352 ± 0.0010 1.180 ± 0.069 1.213 ± 0.048 19.9 ± 1.2 0.662 ± 0.060 XO-1 b 0.0465 ± 0.0013 0.818 ± 0.078 1.135 ± 0.046 15.8 ± 1.5 0.559 ± 0.068 +0.011 +0.11 +0.07 +1.6 +0.058 WASP-1b 0.0417−0.014 1.02−0.12 1.59−0.11 10.0−1.2 0.255−0.037 WASP-2b 0.0301 ± 0.0011 0.841 ± 0.085 1.030 ± 0.059 19.7 ± 2.7 0.77 ± 0.15 HAT-P-1 b 0.0541 ± 0.0015 0.507 ± 0.033 1.179 ± 0.049 9.05 ± 0.66 0.309 ± 0.033 OGLE-TR-10 b 0.0449 ± 0.0017 0.67 ± 0.15 1.28 ± 0.11 10.2 ± 2.7 0.32 ± 0.11 OGLE-TR-56 b 0.0238 ± 0.0014 1.29 ± 0.18 1.20 ± 0.18 22.3 ± 7.0 0.75 ± 0.35 OGLE-TR-111 b 0.0462 ± 0.0016 0.53 ± 0.10 1.069 ± 0.075 11.5 ± 2.5 0.44 ± 0.11 OGLE-TR-132 b 0.0308 ± 0.0016 1.02 ± 0.32 1.28 ± 0.17 15.6 ± 6.1 0.49 ± 0.24 GJ 436 b 0.0282 ± 0.0013 0.0704 ± 0.0069 0.357 ± 0.022 13.7 ± 1.1 1.54 ± 0.20 +0.0020 +0.035 +0.110 +6.8 +0.71 HD 149026 b 0.0427−0.0013 0.353−0.024 0.608−0.047 23.7−6.2 1.57−0.58 HD 189733 b 0.0293 ± 0.0010 1.023 ± 0.074 1.074 ± 0.047 22.0 ± 1.4 0.827 ± 0.080 HD 209458 b 0.0472 ± 0.0011 0.693 ± 0.032 1.376 ± 0.032 9.08 ± 0.17 0.266 ± 0.009

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Table A17. Properties of the stellar components of the TEPs not studied in this work. References are given in Table A19.

£ ¤ Fe −2 System Teff (K) H (dex) MA (M¯) RA (R¯) loggA [ cm s ] ρA (ρ¯) CoRoT-Exo-1 5950 ± 150 −0.30 ± 0.25 0.95 ± 0.15 1.11 ± 0.05 CoRoT-Exo-2 5625 ± 120 +0.0 ± 0.1 0.97 ± 0.06 0.902 ± 0.018 +0.03 +0.01 CoRoT-Exo-4 6190 ± 60 +0.07 ± 0.05 1.16−0.02 1.17−0.03 4.37 ± 0.02 +0.088 +0.13 +0.043 +0.004 HAT-P-2 6290 ± 110 +0.12 ± 0.08 1.308−0.078 1.506−0.096 4.199−0.053 0.439−0.114 +0.044 +0.034 +0.034 +0.38 HAT-P-3 5185 ± 46 +0.27 ± 0.04 0.928−0.054 0.833−0.044 4.564−0.044 1.90−0.42 +0.070 +0.060 +0.019 +0.005 HAT-P-4 5680 ± 80 +0.24 ± 0.08 1.248−0.12 1.596−0.075 4.127−0.028 0.317−0.028 +0.043 +0.046 +0.025 +0.058 HAT-P-5 5960 ± 100 +0.24 ± 0.15 1.157−0.081 1.165−0.052 4.368−0.031 0.729−0.054 +0.064 +0.069 +0.027 +0.069 HAT-P-6 6570 ± 80 −0.13 ± 0.08 1.290−0.066 1.463−0.063 4.218−0.030 0.450−0.061 +0.08 +0.23 +0.04 HAT-P-7 6350 ± 80 +0.26 ± 0.08 1.47−0.05 1.84−0.11 4.07−0.08 +0.03 HAT-P-9 6350 ± 150 +0.12 ± 0.20 1.28 ± 0.13 1.32 ± 0.07 4.29−0.04 +0.012 +0.35 HD-17156 6079 ± 56 +0.24 ± 0.03 1.2 ± 0.1 1.354−0.037 3.47−0.18 Lupus-TR-3 5000 ± 150 0.87 ± 0.04 0.82 ± 0.05 +0.017 +0.020 +0.009 +0.02 OGLE-TR-113 4790 ± 75 +0.09 ± 0.08 0.779−0.015 0.774−0.018 4.552−0.017 1.70−0.21 +0.23 OGLE-TR-182 5924 ± 64 +0.37 ± 0.08 1.14 ± 0.05 1.14−0.06 +0.21 OGLE-TR-211 6325 ± 91 +0.11 ± 0.10 1.33 ± 0.05 1.64−0.07 +0.021 +0.014 +0.017 TrES-3 5650 ± 50 −0.19 ± 0.08 0.915−0.031 0.812−0.025 4.581−0.012 1.754 ± 0.085 +0.060 +0.065 +0.024 TrES-4 6200 ± 75 +0.14 ± 0.09 1.394−0.056 1.816−0.062 4.064 ± 0.021 0.172−0.022 +0.06 +0.05 +0.07 +0.15 WASP-3 6400 ± 100 +0.00 ± 0.20 1.24−0.11 1.31−0.12 4.30−0.03 0.55−0.05 +0.077 +0.040 +0.016 +0.038 WASP-4 5500 ± 150 +0.0 ± 0.2 0.900−0.071 0.937−0.030 4.45−0.029 1.094−0.085 +0.099 +0.073 +0.039 WASP-5 5700 ± 150 +0.0 ± 0.2 0.972−0.079 1.026−0.044 4.403−0.048 +0.09 +0.059 +0.010 WASP-7 6400 ± 100 +0.0 ± 0.1 1.28−0.19 1.236−0.046 4.363−0.047 +0.086 +0.056 +0.05 +0.22 WASP-10 4675 ± 100 +0.03 ± 0.20 0.710−0.071 0.783−0.082 4.50−0.04 1.48−0.18 +0.080 +0.069 +0.026 +0.063 WASP-14 6475 ± 100 +0.0 ± 0.2 1.319−0.170 1.297−0.054 4.332−0.062 0.605−0.094 +0.032 +0.027 +0.020 +0.040 XO-2 5340 ± 80 +0.45 ± 0.05 0.974−0.034 0.971−0.026 4.452−0.022 10.83−0.078 XO-3 6429 ± 50 −0.177 ± 0.027 1.213 ± 0.066 1.377 ± 0.083 4.244 ± 0.041 0.461 ± 0.061 XO-4 6397 ± 70 −0.04 ± 0.03 1.32 ± 0.02 1.55 ± 0.05 4.18 ± 0.07 XO-5 5510 ± 44 +0.25 ± 0.03 1.00 ± 0.03 1.11 ± 0.09 4.34 ± 0.07 0.72 ± 0.14

Table A18. Properties of the planetary components of the TEPs not studied in this work. References are given in Table A19.

−1 System Porb (day) a (AU) Mb (MJup) Rb (RJup) gb ( m s ) ρp (ρJup) Teq (K) CoRoT-Exo-1 b 1.509 1.03 ± 0.12 1.49 ± 0.08 0.31 ± 0.04 1898 ± 50 CoRoT-Exo-2 b 1.743 3.31 ± 0.16 1.465 ± 0.029 1.06 ± 0.03 1537 ± 35 +0.06 CoRoT-Exo-4 b 9.202 0.090 ± 0.001 0.72 ± 0.08 1.19−0.05 0.423 ± 0.12 1074 ± 19 +0.0015 +0.084 +10 +2.0 +61 HAT-P-2 b 5.633 0.0679−0.0014 8.72 ± 0.36 1.003−0.066 234−39 8.6−1.9 1398−33 +0.00060 +0.024 +0.043 +3.0 +0.15 +49 HAT-P-3 b 2.900 0.03882−0.00077 0.596−0.026 0.899−0.049 20.4−3.1 0.82−0.11 1127−39 +0.00081 +0.033 +0.049 +0.39 +0.052 +30 HAT-P-4 b 3.057 0.04438−0.0015 0.671−0.044 1.274−0.060 10.47−0.54 0.325−0.049 1686−26 +0.00049 +0.051 +1.9 +0.097 +33 HAT-P-5 b 2.788 0.04071−0.00097 1.06 ± 0.11 1.254−0.056 16.6−1.8 0.532−0.081 1539−32 +0.00085 +0.053 +0.064 +0.069 +32 HAT-P-6 b 3.826 0.05237−0.00090 1.059−0.052 1.330−0.058 14.8 ± 1.0 0.450−0.061 1675−31 +0.077 +0.195 +4.1 +0.14 +150 HAT-P-7 b 2.205 0.0377 ± 0.0005 1.776−0.049 1.363−0.087 20.4−3.4 0.71−0.19 2730−100 HAT-P-9 b 3.923 0.053 ± 0.002 0.78 ± 0.09 1.40 ± 0.06 9.8 ± 1.0 0.28 ± 0.05 1530 ± 40 +0.22 +0.016 +0.35 HD-17156 b 21.217 0.1594 ± 0.0012 3.09−0.17 0.964−0.027 11.6 ± 5.7 3.47−0.18 Lupus-TR-3 b 3.914 0.0464 ± 0.008 0.81 ± 0.18 0.89 ± 0.07 1.1 ± 0.3 +0.0086 +0.028 +3.7 +0.14 +30 OGLE-TR-113 b 1.432 0.0677−0.0087 1.26 ± 0.16 1.093−0.019 26.2−3.6 0.97−0.13 1341−25 +0.24 OGLE-TR-182 b 3.979 0.051 ± 0.001 1.01 ± 0.15 1.13−0.08 +0.18 +0.12 OGLE-TR-211 b 3.677 0.051 ± 0.001 1.03 ± 0.20 1.36−0.09 0.44−0.19 +0.00017 +0.062 +0.033 +1.5 +0.089 +26 TrES-3 b 1.306 0.02272−0.00026 1.938−0.063 1.312−0.041 28.3−1.4 0.858−0.068 1623−25 +0.00072 +0.073 +0.064 +0.66 +0.024 TrES-4 b 3.554 0.05092−0.00069 0.920−0.072 1.751−0.062 7.45−0.64 0.172−0.022 1785 ± 29 +0.0005 +0.08 +0.07 +5.4 +0.28 +33 WASP-3b 1.847 0.0317−0.0010 1.76−0.14 1.31−0.14 23.4−2.1 0.78−0.09 1960−76 +0.087 +0.068 +0.75 +0.032 +24 WASP-4b 1.338 0.0230 ± 0.001 1.215−0.079 1.416−0.043 13.87−1.04 0.420−0.044 1761−9 +0.00088 +0.13 +0.19 +3.2 +0.19 +51 WASP-5b 1.628 0.02683−0.00075 1.58−0.08 1.090−0.24 30.5−4.1 1.22−0.24 1753−36 +0.0014 +0.12 +0.048 +4.4 +0.25 +35 WASP-7b 4.955 0.0618−0.0033 0.96−0.18 0.915−0.040 26.4−4.0 1.26−0.21 1379−23 +0.0014 +0.075 +5.1 +0.27 +25 WASP-10b 3.093 0.037−0.0013 3.06 ± 0.23 1.29−0.082 41.7−4.5 1.42−0.24 1123−26 +0.001 +0.43 +0.080 +9 +0.53 +51 WASP-14b 2.244 0.037−0.002 7.73−0.67 1.259−0.058 111−13 3.87−0.67 1784−29 +0.00040 +0.029 +1.5 +0.081 +24 XO-2 b 2.616 0.03684−0.00043 0.566 ± 0.055 0.983−0.028 14.7−1.5 0.597−0.073 1319−23 +1.4 XO-3 b 3.192 0.0454 ± 0.00082 11.79 ± 0.59 1.217 ± 0.073 197 ± 19 6.5−1.0 1710 ± 46 XO-4 b 4.125 0.0555 ± 0.00011 1.72 ± 0.20 1.34 ± 0.048 XO-5 b 4.188 0.0508 ± 0.0005 1.15 ± 0.08 1.15 ± 0.12 22 ± 5 0.82 ± 0.24 1244 ± 48

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Table A19. References to Tables A17 and A18.

System Discovery paper Additional references

CoRoT-Exo-1 Barge et al. (2008) CoRoT-Exo-2 Alonso et al. (2008) Bouchy et al. (2008) CoRoT-Exo-4 Aigrain et al. (2008) Moutou et al. (2008) HAT-P-2 Bakos et al. (2007c) TWH08 HAT-P-3 Torres et al. (2007) TWH08 HAT-P-4 Kovacs´ et al. (2007) TWH08 HAT-P-5 Bakos et al. (2007b) TWH08 HAT-P-6 Noyes et al. (2008) TWH08 HAT-P-7 Pal´ et al. (2008) HAT-P-9 Shporer et al. (2008b) HD-17156 Barbieri et al. (2007) Gillon et al. (2008) Lupus-TR-3 Weldrake et al. (2008) OGLE-TR-113 Bouchy et al. (2004) TWH08 OGLE-TR-182 Pont et al. (2008) OGLE-TR-211 Udalski et al. (2008) TrES-3 O’Donovan et al. (2007) TWH08 TrES-4 Mandushev et al. (2007) TWH08 WASP-3 Pollacco et al. (2008) WASP-4 Wilson et al. (2008) WASP-5 Anderson et al. (2008) WASP-7 Hellier et al. (2008) WASP-10 Christian et al. (2008) WASP-14 Joshi et al. (2008) XO-2 Burke et al. (2007) TWH08 XO-3 Johns-Krull et al. (2008) Winn et al. (2008b) XO-4 McCullough et al. (2008) XO-5 Burke et al. (2008)

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